text:
Conformity
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Conformity is the act of matching attitudes, beliefs, and behaviors to group norms.[1] Norms are implicit, specific rules, shared by a group of individuals, that guide their interactions with others. This tendency to conform occurs in small groups and/or society as a whole, and may result from subtle unconscious influences, or direct and overt social pressure. Conformity can occur in the presence of others, or when an individual is alone. For example, people tend to follow social norms when eating or watching television, even when alone.
People often conform from a desire for security within a group—typically a group of a similar age, culture, religion, or educational status. This is often referred to as groupthink: a pattern of thought characterized by self-deception, forced manufacture of consent, and conformity to group values and ethics, which ignores realistic appraisal of other courses of action. Unwillingness to conform carries the risk of social rejection. Conformity is often associated with adolescence and youth culture, but strongly affects humans of all ages.[2]
Although peer pressure may manifest negatively, conformity can be regarded as either good or bad. Driving on the correct side of the road could be seen as beneficial conformity.[3] With the right environmental influence, conforming, in early childhood years, allows one to learn and thus, adopt the appropriate behaviours necessary to interact and develop correctly within one's society.[4] Conformity influences formation and maintenance of social norms, and helps societies function smoothly and predictably via the self-elimination of behaviors seen as contrary to unwritten rules. In this sense it can be perceived as a positive force that prevents acts that are perceptually disruptive or dangerous.
As conformity is a group phenomenon, factors such as group size, unanimity, cohesion, status, prior commitment and public opinion help determine the level of conformity an individual displays.
Contents
[hide]
1 Peer
2 Social responses
3 Main experiments
3.1 Sherif's experiment (1936)
3.2 Asch's experiment (1951)
4 Varieties
4.1 Informational influence
4.2 Normative influence
5 Minority influence
6 Specific predictors
6.1 Culture
6.2 Gender
6.3 Age
6.4 Size of the group
6.5 Different stimuli
6.6 Neural correlates
7 See also
8 References
9 External links
Peer[edit]
Some adolescents gain acceptance and recognition from their peers by conformity. This peer moderated conformity increases from the transition of childhood to adolescence.[5]
Social responses[edit]
According to Donelson Forsyth, after submitting to group pressures, individuals may find themselves facing one of several responses to conformity. These types of responses to conformity vary in their degree of public agreement versus private agreement.
When an individual finds themselves in a position where they publicly agree with the group's decision yet privately disagrees with the group's consensus, they are experiencing compliance or acquiescence. In turn, conversion, otherwise known as private acceptance, involves both publicly and privately agreeing with the group's decision. Thus, this represents a true change of opinion to match the majority.
Another type of social response, which does not involve conformity with the majority of the group, is called convergence. In this type of social response, the group member agrees with the group's decision from the outset and thus does not need to shift their opinion on the matter at hand.[6]
In addition, Forsyth shows that nonconformity can also fall into one of two response categories. Firstly, an individual who does not conform to the majority can display independence. Independence, or dissent, can be defined as the unwillingness to bend to group pressures. Thus, this individual stays true to his or her personal standards instead of the swaying toward group standards. Secondly, a nonconformist could be displaying anticonformity or counterconformity which involves the taking of opinions that are opposite to what the group believes. This type of nonconformity can be motivated by a need to rebel against the status quo instead of the need to be accurate in one's opinion.
To conclude, social responses to conformity can be seen to vary along a continuum from conversion to anticonformity. For example, a popular experiment in conformity research, known as the Asch situation or Asch conformity experiments, primarily includes compliance and independence. Also, other responses to conformity can be identified in groups such as juries, sports teams and work teams.[6]
Main experiments[edit]
Sherif's experiment (1936)[edit]
Muzafer Sherif was interested in knowing how many people would change their opinions to bring them in line with the opinion of a group. In his experiment, participants were placed in a dark room and asked to stare at a small dot of light 15 feet away. They were then asked to estimate the amount it moved. The trick was there was no movement, it was caused by a visual illusion known as the autokinetic effect. On the first day, each person perceived different amounts of movement, but from the second to the fourth day, the same estimate was agreed on and others conformed to it.[7] Sherif suggested this was a simulation for how social norms develop in a society, providing a common frame of reference for people.
Subsequent experiments were based on more realistic situations. In an eyewitness identification task, participants were shown a suspect individually and then in a lineup of other suspects. They were given one second to identify him, making it a difficult task. One group was told that their input was very important and would be used by the legal community. To the other it was simply a trial. Being more motivated to get the right answer increased the tendency to conform. Those who wanted to be more accurate conformed 51% of the time as opposed to 35% in the other group.[8]
Asch's experiment (1951)[edit]
Main article: Asch conformity experiments
Which line matches the first line, A, B, or C? In the Asch conformity experiments, people frequently followed the majority judgment, even when the majority was wrong.
Solomon E. Asch conducted a modification of Sherif’s study, assuming that when the situation was very clear, conformity would be drastically reduced. He exposed people in a group to a series of lines, and the participants were asked to match one line with a standard line. All participants except one were accomplices and gave the wrong answer in 12 of the 18 trials.[9]
The results showed a surprisingly high degree of conformity: 74% of the participants conformed on at least one trial. On average people conformed one third of the time.[9] A question is how the group would affect individuals in a situation where the correct answer is less obvious.[10]
After his first test, Asch wanted to investigate whether the size or unanimity of the majority had greater influence on test subjects. "Which aspect of the influence of a majority is more important – the size of the majority or its unanimity? The experiment was modified to examine this question. In one series the size of the opposition was varied from one to 15 persons."[11] The results clearly showed that as more people opposed the subject, the subject became more likely to conform. However, the increasing majority was only influential up to a point: from three or more opponents, there is more than 30% of conformity.[9]
Varieties[edit]
Harvard psychologist Herbert Kelman identified three major types of conformity.[12]
Compliance is public conformity, while possibly keeping one's own original beliefs for yourself. Compliance is motivated by the need for approval and the fear of being rejected.
Identification is conforming to someone who is liked and respected, such as a celebrity or a favorite uncle. This can be motivated by the attractiveness of the source,[12] and this is a deeper type of conformism than compliance.
Internalization is accepting the belief or behavior and conforming both publicly and privately, if the source is credible. It is the deepest influence on people and it will affect them for a long time.
Although Kelman's distinction has been influential, research in social psychology has focused primarily on two varieties of conformity. These are informational conformity, or informational social influence, and normative conformity, also called normative social influence. In Kelman's terminology, these correspond to internalization and compliance, respectively. There are naturally more than two or three variables in society influential on human psychology and conformity; the notion of "varieties" of conformity based upon "social influence" is ambiguous and indefinable in this context.
For Deutsch and Gérard (1955), conformity results from a motivational conflict (between the fear of being socially rejected and the wish to say what we think is correct) that leads to the normative influence, and a cognitive conflict (others create doubts in what we think) which leads to the informational influence.[13]
Informational influence[edit]
Main article: Informational social influence
Informational social influence occurs when one turns to the members of one's group to obtain and accept accurate information about reality. A person is most likely to use informational social influence in certain situations: when a situation is ambiguous, people become uncertain about what to do and they are more likely to depend on others for the answer; and during a crisis when immediate action is necessary, in spite of panic. Looking to other people can help ease fears, but unfortunately they are not always right. The more knowledgeable a person is, the more valuable they are as a resource. Thus people often turn to experts for help. But once again people must be careful, as experts can make mistakes too. Informational social influence often results in internalization or private acceptance, where a person genuinely believes that the information is right.[7]
Normative influence[edit]
Main article: Normative social influence
Normative social influence occurs when one conforms to be liked or accepted by the members of the group. This need of social approval and acceptance is part of our state of humans.[7] In addition to this, we know that when people do not conform with their group and therefore are deviants, they are less liked and even punished by the group.[14] Normative influence usually results in public compliance, doing or saying something without believing in it. The experiment of Asch in 1951 is one example of normative influence
In a reinterpretation of the original data from these experiments Hodges and Geyer (2006)[15] found that Asch's subjects were not so conformist after all: The experiments provide powerful evidence for people's tendency to tell the truth even when others do not. They also provide compelling evidence of people's concern for others and their views. By closely examining the situation in which Asch's subjects find themselves they find that the situation places multiple demands on participants: They include truth (i.e., expressing one's own view accurately), trust (i.e., taking seriously the value of others' claims), and social solidarity (i.e., a commitment to integrate the views of self and others without deprecating either). In addition to these epistemic values, there are multiple moral claims as well: These include the need for participants to care for the integrity and well-being of other participants, the experimenter, themselves, and the worth of scientific research.
Deutsch & Gérard (1955) designed different situations that variated from Asch' experiment and found that when participants were writing their answer privately, they were giving the correct one[13]
Normative influence, a function of social impact theory, has three components.[16] The number of people in the group has a surprising effect. As the number increases, each person has less of an impact. A group's strength is how important the group is to a person. Groups we value generally have more social influence. Immediacy is how close the group is in time and space when the influence is taking place. Psychologists have constructed a mathematical model using these three factors and are able to predict the amount of conformity that occurs with some degree of accuracy.[17]
Baron and his colleagues conducted a second eyewitness study that focused on normative influence. In this version, the task was easier. Each participant had five seconds to look at a slide instead of just one second. Once again, there were both high and low motives to be accurate, but the results were the reverse of the first study. The low motivation group conformed 33% of the time (similar to Asch's findings). The high motivation group conformed less at 16%. These results show that when accuracy is not very important, it is better to get the wrong answer than to risk social disapproval.
An experiment using procedures similar to Asch's found that there was significantly less conformity in six-person groups of friends as compared to six-person groups of strangers.[18] Because friends already know and accept each other, there may be less normative pressure to conform in some situations. Field studies on cigarette and alcohol abuse, however, generally demonstrate evidence of friends exerting normative social influence on each other.[19]
Minority influence[edit]
Main article: Minority influence
Although conformity generally leads individuals to think and act more like groups, individuals are occasionally able to reverse this tendency and change the people around them. This is known as minority influence, a special case of informational influence. Minority influence is most likely when people can make a clear and consistent case for their point of view. If the minority fluctuates and shows uncertainty, the chance of influence is small. However, a minority that makes a strong, convincing case increases the probability of changing the majority's beliefs and behaviors.[20] Minority members who are perceived as experts, are high in status, or have benefited the group in the past are also more likely to succeed.
Another form of minority influence can sometimes override conformity effects and lead to unhealthy group dynamics. A 2007 review of two dozen studies by the University of Washington found that a single "bad apple" (an inconsiderate or negligent group member) can substantially increase conflicts and reduce performance in work groups. Bad apples often create a negative emotional climate that interferes with healthy group functioning. They can be avoided by careful selection procedures and managed by reassigning them to positions that require less social interaction.[21]
Specific predictors[edit]
Culture[edit]
Stanley Milgram found that individuals in Norway (from a collectivistic culture) exhibited a higher degree of conformity than individuals in France (from an individualistic culture).[22] Similarly, Berry studied two different populations: the Temne (collectivists) and the Inuit (individualists) and found that the Temne conformed more than the Inuit when exposed to a conformity task.[23]
Bond and Smith compared 134 studies in a meta-analysis and found that Japan and Brazil were two nations that conformed a lot whereas Europe and the United States of America did not as much.[24] Bond and Smith also reported that conformity has declined in the United States over time.
Gender[edit]
Societal norms often establish gender differences and researchers have reported differences in the way men and women conform to social influence.[25][26][27][28][29][30][31] For example, Alice Eagly and Linda Carli performed a meta-analysis of 148 studies of influenceability. They found that women are more persuadable and more conforming than men in group pressure situations that involve surveillance.[32] Eagly has proposed that this sex difference may be due to different sex roles in society.[33] Women are generally taught to be more agreeable whereas men are taught to be more independent.
The composition of the group plays a role in conformity as well. In a study by Reitan and Shaw, it was found that men and women conformed more when there were participants of both sexes involved versus participants of the same sex. Subjects in the groups with both sexes were more apprehensive when there was a discrepancy amongst group members, and thus the subjects reported that they doubted their own judgments.[26] Sistrunk and McDavid made the argument that women conformed more because of a methodological bias.[34] They argued that because stereotypes used in studies are generally male ones (sports, cars..) more than female ones (cooking, fashion..), women are feeling uncertain and conformed more, which was confirmed by their results.
Age[edit]
Research has noted age differences in conformity. For example, research with Australian children and adolescents ages 3 to 17 discovered that conformity decreases with age.[35] Another study examined individuals that were ranged from ages 18 to 91.[36] The results revealed a similar trend – older participants displayed less conformity when compared to younger participants.
In the same way that gender has been viewed as corresponding to status, age has also been argued to have status implications. Berger, Rosenholtz and Zelditch suggest that age as a status role can be observed among college students. Younger students, such as those in their first year in college, are treated as lower-status individuals and older college students are treated as higher-status individuals.[37] Therefore, given these status roles, it would be expected that younger individuals (low status) conform to the majority whereas older individuals (high status) would be expected not to conform [38]
Researchers have also reported an interaction of gender and age on conformity.[39] Eagly and Chrvala examined the role of age (under 19 years vs. 19 years and older), gender and surveillance (anticipating responses to be shared with group members vs. not anticipating responses being shared) on conformity to group opinions. They discovered that among participants that were 19 years or older, females conformed to group opinions more so than males when under surveillance (i.e., anticipated that their responses would be shared with group members). However, there were no gender differences in conformity among participants who were under 19 years of age and in surveillance conditions. There were also no gender differences when participants were not under surveillance. In a subsequent research article, Eagly suggests that women are more likely to conform than men because of lower status roles of women in society. She suggests that more submissive roles (i.e., conforming) are expected of individuals that hold low status roles.[38] Still, Eagly and Chrvala's results do conflict with previous research which have found higher conformity levels among younger rather than older individuals.
Size of the group[edit]
Although conformity pressures generally increase as the size of the majority increases, a meta-analysis suggests that conformity pressures in Asch's experiment peak once the majority reaches about four or five in number.[40] Moreover, a study suggests that the effects of group size depend on the type of social influence operating.[41] This means that in situations where the group is clearly wrong, conformity will be motivated by normative influence; the participants will conform in order to be accepted by the group. A participant may not feel much pressure to conform when the first person gives an incorrect response. However, conformity pressure will increase as each additional group member also gives the same incorrect response.[41]
Different stimuli[edit]
In 1961 Stanley Milgram published a study in which he utilized Asch's conformity paradigm using audio tones instead of lines; he conducted his study in Norway and France.[22] He found substantially higher levels of conformity than Asch, with participants conforming 50% of the time in France and 62% of the time in Norway during critical trials. Milgram also conducted the same experiment once more, but told participants that the results of the study would be applied to the design of aircraft safety signals. His conformity estimates were 56% in Norway and 46% in France, suggesting that individuals conformed slightly less when the task was linked to an important issue. Stanley Milgram's study demonstrated that Asch's study could be replicated with other stimuli, and that in the case of tones, there was a high degree of conformity.
Neural correlates[edit]
Evidence has been found for the involvement of the posterior medial frontal cortex (pMFC) in conformity,[42] an area associated with memory and decision-making. For example, Klucharev et al.[43] revealed in their study that by using repetitive transcranial magnetic stimulation on the pMFC, participants reduced their tendency to conform to the group, suggesting a causal role for the brain region in social conformity. In another study, the mPFC was linked to normative social influence, whilst the activity in the caudate was regarded as an index of informational influence.[44]
The amygdala and hippocampus have also been found to be recruited when individuals participated in a social manipulation experiment involving long-term memory.[45] Several other areas have further been suggested to play a role in conformity, including the insula, the temporoparietal junction, the ventral striatum, and the anterior and posterior cingulate cortices.[46][47][48][49][50]
More recent work[51] stresses the role of orbitofrontal cortex (OFC) in conformity not only at the time of social influence,[52] but also later on, when participants are given an opportunity to conform by selecting an action. In particular, Charpentier et al. found that the OFC mirrors the exposure to social influence at a subsequent time point, when a decision is being made without the social influence being present. The tendency to conform has also been observed in the structure of the OFC, with a greater grey matter volume in high conformers.[53]
See also[edit]
Psychology portal
Sociology portal
Authoritarian personality
Countersignaling
Cultural assimilation
Milieu control
Propaganda: The Formation of Men's Attitudes
Spiral of silence
References[edit]
Jump up ^ Cialdini, R. B.; Goldstein, N. J. (2004). "Social influence: Compliance and conformity" (PDF). Annual Review of Psychology. 55: 591–621. doi:10.1146/annurev.psych.55.090902.142015.
Jump up ^ McLeod, S (November 2011). "Conformity". Simply psychology.
Jump up ^ Aronson, E; Wilson, T. D.; Akert, R. M. (2007). Social Psychology (6th ed.). Upper Saddle River, NJ: Pearson Prentice Hall. ISBN 978-0-13-233487-7.
Jump up ^ L, G (March 1931). "Conformity". Peabody Journal of Education. Taylor & Francis, Ltd. 8 (5): 312. doi:10.1080/01619563109535026. JSTOR 1488401.
Jump up ^ Brown, Bradford (1986). "Perceptions of peer pressure, peer conformity dispositions, and self-reported behavior among adolescents". Developmental Psychology. 22 (4): 521–530. doi:10.1037/0012-1649.22.4.521.
^ Jump up to: a b Forsyth, D. R. (2013). Group dynamics. New York: Wadsworth. ISBN 978-1-13-395653-2. [Chapter 7]
^ Jump up to: a b c Hogg, M. A.; Vaughan, G. M. (2005). Social psychology. Harlow: Pearson/Prentice Hall.
Jump up ^ Baron, R. S.; Vandello, J. A.; Brunsman, B. (1996). "The forgotten variable in conformity research: Impact of task importance on social influence". Journal of Personality and Social Psychology. 71 (5): 915–927. doi:10.1037/0022-3514.71.5.915.
^ Jump up to: a b c Asch, S. E. (1955). "Opinions and Social Pressure". Scientific American. 193 (5): 31–35. doi:10.1038/scientificamerican1155-31.
Jump up ^ Guimond, S (2010). Psychologie Sociale : Perspective Multiculturelle. Warve:: Mardaga. pp. 19–28.
Jump up ^ Asch, S. E. (1952). Social Psychology. Englewood Cliffs, NJ:: Prentice Hal.
^ Jump up to: a b Kelman, H. C (1958). "Compliance, Identification, and Internalization: Three Processes of Attitude Change". Journal of Conflict Resolution. 2 (1): 51–60. doi:10.1177/002200275800200106.
^ Jump up to: a b Deutsch, M; Gérard, H. B (1955). "A study of normative and informational social influences upon individual judgement". Journal of Abnormal Psychology. 51 (3): 629–636. doi:10.1037/h0046408. PMID 13286010.
Jump up ^ Schachter,, S (1951). "Deviation, Rejection, and communication". Journal of Abnormal and Social Psychology. 46: 190–208. doi:10.1037/h0062326.
Jump up ^ Hodges,, B. H.; Geyer, A. L. (2006). "A Nonconformist Account of the Asch Experiments: Values, Pragmatics, and Moral Dilemmas". Personality and Social Psychology Review. 10 (1): 2–19. doi:10.1207/s15327957pspr1001_1.
Jump up ^ Latané,, B (1981). "The psychology of social impact". American Psychologist. 36 (4): 343–356. doi:10.1037/0003-066x.36.4.343.
Jump up ^ Forgas, J. P.; Williams, K. D (2001). Social influence: Direct and indirect processes. The Sydney symposium of social psychology. New York:: Psychology Press. pp. 61–76.
Jump up ^ McKelvey, W.; Kerr, N. H. (1988). "Differences in conformity among friends and strangers". Psychological Reports. 62 (3): 759–762. doi:10.2466/pr0.1988.62.3.759.
Jump up ^ Urberg,, K. A.; Degirmencioglu, S. M.; Pilgrim, C. (1997). "Close friend and group influence on adolescent cigarette smoking and alcohol use". Developmental Psychology. 33 (5): 834–844. doi:10.1037/0012-1649.33.5.834.
Jump up ^ Moscovici,, S. N. (1974). "Minority influence". Social psychology: Classic and contemporary integrations. Chicago:: Rand McNally. pp. 217–249.
Jump up ^ Felps, W; Mitchell, T R.; Byington, E (2006). "How, When, and Why Bad Apples Spoil the Barrel: Negative Group Members and Dysfunctional". GroupsResearch in Organizational Behavior. 27: 175–222. doi:10.1016/s0191-3085(06)27005-9.
^ Jump up to: a b Milgram, S (1961). "Nationality and conformity". Scientific American. 205: 6.
Jump up ^ Berry,, J W. (1967). "Independence and conformity in subsistence-level societies". Journal of Personality and Social Psychology. 7: 415–418. doi:10.1037/h0025231.
Jump up ^ Bond,, M. H; Smith, P. B. (1996). "Culture and Conformity: A meta-analysis of studies using the Asch's (1952b, 1956) line judgement task". Psychological Bulletin. 119: 111–137. doi:10.1037/0033-2909.119.1.111.
Jump up ^ Bond, R.; Smith, P.B. (1996). "Culture and conformity: A meta-analysis of studies using Asch's (1952b, 1956) line judgement task" (PDF). Psychological Bulletin. 119 (1): 111–137. doi:10.1037/0033-2909.119.1.111.
^ Jump up to: a b Reitan,, H; Shaw, M (1964). "Group Membership, Sex-Composition of the Group, and Conformity Behavior". The Journal of Social Psychology. 64: 45–51. doi:10.1080/00224545.1964.9919541.
Jump up ^ Applezweig, M H; Moeller, G (1958). Conforming behavior and personality variables. New London: Connecticut College.
Jump up ^ Beloff,, H (1958). "Two forms of social conformity: Acquiescence and conventionality". The Journal of Abnormal and Social Psychology. 56 (1): 99–104. doi:10.1037/h0046604.
Jump up ^ Coleman,, J; Blake, R R; Mouton, J S (1958). "Task difficulty and conformity pressures". The Journal of Abnormal and Social Psychology. 57 (1): 120–122. doi:10.1037/h0041274.
Jump up ^ Cooper, H.M. (1979). "Statistically combining independent studies: A meta-analysis of sex differences in conformity research". Journal of Personality and Social Psychology. 37: 131–146. doi:10.1037/0022-3514.37.1.131.
Jump up ^ Eagly, A.H. (1978). "Sex differences in influenceability". Psychological Bulletin. 85: 86–116. doi:10.1037/0033-2909.85.1.86.
Jump up ^ Eagly,, A. H; Carli, L. L (1981). "Sex of researchers and sex-typed communications as determinants of sex differences in influenceability: A meta-analysis of social influence studies". Psychological Bulletin. 90 (1): 1–20. doi:10.1037/0033-2909.90.1.1.
Jump up ^ Eagly,, A. H. (1987). Sex differences in social behavior: A social role interpretation. Hillsdale, NJ: Erlbaum.
Jump up ^ Sistrunk,, F; McDavid, J. W (1971). "Sex variable in conforming behavior". Journal of Personality and Social Psychology. 17 (2): 200–207. doi:10.1037/h0030382.
Jump up ^ Walker, M.; Andrade, M. (1996). "Conformity in the Asch Task as a Function of Age". The Journal of Social Psychology. 136 (3): 367–372. doi:10.1080/00224545.1996.9714014. PMID 8758616.
Jump up ^ Pasupathi, M. (1999). "Age differences in response to conformity pressure for emotional and nonemotional material". Psychology and aging. 14 (1): 170–174. doi:10.1037/0882-7974.14.1.170. PMID 10224640.
Jump up ^ Berger, J.; Rosenholtz, S.J.; Zelditch, M. (1980). "Status organizing processes". Annual Review of Sociology. 6: 479–508. doi:10.1146/annurev.so.06.080180.002403.
^ Jump up to: a b Eagly, A.H.; Wood, W. (1982). "Inferred sex differences in status as a determinant of gender stereotypes about social influence". Journal of Personality and Social Psychology. 43 (5): 915–928. doi:10.1037/0022-3514.43.5.915.
Jump up ^ Eagly, A.H.; Chrvala, C. (1980). "Sex differences in conformity: Status and gender role interpretations". Psychology of Women Quarterly. 10: 203–220. doi:10.1111/j.1471-6402.1986.tb00747.x.
Jump up ^ Bond, R.; Smith, P. B. (1996). "Culture and conformity: A meta-analysis of studies using Asch's (1952b, 1956) Line Judgement task" (PDF). Psychological Bulletin. 119: 111–137. doi:10.1037/0033-2909.119.1.111.
^ Jump up to: a b Campbell, J. D.; Fairey, P. J. (1989). "Informational and normative routes to conformity: The effect of faction size as a function of norm extremity and attention to the stimulus". Journal of Personality and Social Psychology. 57: 457–468. doi:10.1037/0022-3514.57.3.457.
Jump up ^ Izuma, K (2013). "The neural basis of social influence and attitude change". Current Opinion in Neurobiology. 23 (3): 456–462. doi:10.1016/j.conb.2013.03.009.
Jump up ^ Klucharev, V.; Munneke, M. A.; Smidts, A.; Fernández, G. (2011). "Downregulation of the posterior medial frontal cortex prevents social conformity". The Journal of Neuroscience. 31 (33): 11934–11940. doi:10.1523/JNEUROSCI.1869-11.2011.
Jump up ^ Mason, M. F.; Dyer, R.; Norton, M. I. (2009). "Neural mechanisms of social influence". Organizational Behavior and Human Decision Processes. 110 (2): 152–159. doi:10.1016/j.obhdp.2009.04.001.
Jump up ^ Edelson, M.; Sharot, T.; Dolan, R. J.; Dudai, Y. (2011). "Following the crowd: brain substrates of long-term memory conformity". Science. 333 (6038): 108–111. doi:10.1126/science.1203557. PMC 3284232  . PMID 21719681.
Jump up ^ Stallen, M.; Smidts, A.; Sanfey, A. G. (2013). "Peer influence: neural mechanisms underlying in-group conformity". Frontiers in Human Neuroscience. 7. doi:10.3389/fnhum.2013.00050.
Jump up ^ Falk, E. B.; Way, B. M.; Jasinska, A. J. (2012). "An imaging genetics approach to understanding social influence". Frontiers in Human Neuroscience. 6: 168. doi:10.3389/fnhum.2012.00168. PMC 3373206  . PMID 22701416.
Jump up ^ Berns, G. S.; Chappelow, J.; Zink, C. F.; Pagnoni, G.; Martin-Skurski, M. E.; Richards, J. (2005). "Neurobiological correlates of social conformity and independence during mental rotation". Biological Psychiatry. 58 (3): 245–253. doi:10.1016/j.biopsych.2005.04.012. PMID 15978553.
Jump up ^ Berns, G. S.; Capra, C. M.; Moore, S.; Noussair, C. (2010). "Neural mechanisms of the influence of popularity on adolescent ratings of music". NeuroImage. 49 (3): 2687–2696. doi:10.1016/j.neuroimage.2009.10.070. PMC 2818406  . PMID 19879365.
Jump up ^ Burke, C. J.; Tobler, P. N.; Schultz, W.; Baddeley, M. (2010). "Striatal BOLD response reflects the impact of herd information on financial decisions". Frontiers in Human Neuroscience. 4: 48. doi:10.3389/fnhum.2010.00048. PMC 2892997  . PMID 20589242.
Jump up ^ Charpentier, C.; Moutsiana, C.; Garrett, N.; Sharot, T. (2014). "The Brain's Temporal Dynamics from a Collective Decision to Individual Action". Journal of Neuroscience. 34 (17): 5816–5823. doi:10.1523/JNEUROSCI.4107-13.2014.
Jump up ^ Zaki, J.; Schirmer, J.; Mitchell, J. P. (2011). "Social influence modulates the neural computation of value". Psychological Science. 22 (7): 894–900. doi:10.1177/0956797611411057.
Jump up ^ Campbell-Meiklejohn, D. K.; Kanai, R.; Bahrami, B.; Bach, D. R.; Dolan, R. J.; Roepstorff, A.; Frith, C. D. (2012). "Structure of orbitofrontal cortex predicts social influence". Current Biology. 22 (4): R123–R124. doi:10.1016/j.cub.2012.01.012.
External links[edit]
Quotations related to Conformity at Wikiquote
[show]
v
t
e
Conformity
Group pressures
Authoritarian personality
Bandwagon effect
Collectivism
Coercive persuasion
Consensus reality
Contagion
Behavioral
Crime
Hysterical
Suicide
Groupthink
Hazing
Herd mentality
Indoctrination
Memory conformity
Milieu control
Mobbing
Nationalism
Normalization
Normative social influence
Ostracism
Panopticon
Patriotism
Peer pressure
Peer review
Pluralistic ignorance
Propaganda
Right-wing authoritarianism
Scapegoating
Shunning
Social influence
Socialization
Spiral of silence
Teasing
Tyranny of the majority
Xeer
Conforming oneself
Compliance
Countersignaling
Herd behavior
Internalisation
Social proof
Obedience
Experiments
Asch conformity experiments
Milgram experiment
Stanford prison experiment
Counterconformity
Anti-authoritarianism
Antisocial tendencies
Auto-segregation
Civil disobedience
Cosmopolitanism
Counterculture
Culture jamming
Deviance
Eclecticism
Eccentricity
Hermit
Idiosyncrasy
Individualism
Rebellion
Ritual clown
Satire
Shock value
[show]
v
t
e
Culture
Outline
Sciences
Cultural anthropology
Cultural astronomy
Cultural ecology
Cultural geography
Cultural neuroscience
Cultural studies
Culturology
Culture theory
Neuroculture
Subfields
Bioculture
Cross-cultural studies
Cross-cultural communication
Cross-cultural leadership
Cross-cultural psychiatry
Cross-cultural psychology
Cultural analytics
Cultural economics
Cultural entomology
Cultural health
Cultural history
Cultural mapping
Cultural mediation
Cultural psychology
Culturomics
Intercultural learning
Intercultural relations
Philosophy of culture
Popular culture studies
Semiotics of culture
Sociology of culture
Sound culture
Theology of culture
Transcultural nursing
Types
Constructed culture
Dominant culture
Folk culture
High culture
Individualistic culture
Legal culture
Low culture
Microculture
Official culture
Political culture
Civic
Popular culture
Urban
Primitive culture
Subculture
Alternative culture
list
Super culture
Vernacular culture
Culture by location
Aspects
Acculturation
Cultural appropriation
Cultural area
Cultural artifact
Cultural baggage
Cultural behavior
Cultural bias
Cultural capital
Cross-cultural
Cultural communication
Cultural conflict
Cultural cringe
Cultural dissonance
Cultural emphasis
Cultural framework
Cultural heritage
Cultural icon
Cultural identity
Cultural industry
Cultural invention
Cultural landscape
Cultural learning
Cultural leveling
Cultural memory
Cultural pluralism
Cultural practice
Cultural property
Cultural reproduction
Cultural system
Cultural technology
Cultural universal
Cultureme
Enculturation
High- and low-context cultures
Interculturality
Manuscript culture
Material culture
Non-material culture
Organizational culture
Print culture
Protoculture
Safety culture
Technoculture
Trans-cultural diffusion
Transculturation
Visual culture
Politics
Colonial mentality
Consumer capitalism
Cross cultural sensitivity
Cultural assimilation
Cultural attaché
Cultural backwardness
Cultural Bolshevism
Cultural conservatism
Cultural contracts
Cultural deprivation
Cultural diplomacy
Cultural environmentalism
Cultural exception
Cultural feminism
Cultural genocide
Cultural globalization
Cultural hegemony
Cultural imperialism
Cultural intelligence
Cultural liberalism
Cultural nationalism
Cultural pessimism
Cultural policy
Cultural racism
Cultural radicalism
Cultural retention
Cultural Revolution
Cultural rights
Cultural safety
Cultural silence
Cultural subsidy
Cultural Zionism
Culture change
Culture minister
Culture of fear
Culture war
Deculturalization
Dominator culture
Interculturalism
Intraculturalism
Monoculturalism
Multiculturalism
Biculturalism
Pluriculturalism
Security culture
Transculturism
Related
Animal culture
Archaeological culture
Bennett scale
Bullying culture
Cannabis culture
Circuit of culture
Coffee culture
Cross-cultural
Cultural center
Cultural Christian
Cultural Mormon
Cultural competence
Cultural critic
Cultural Detective
Cultural determinism
Cultural diversity
Cultural encoding
Cultural evolutionism
Cultural Hindu
Cultural homogenization
Cultural institution
Cultural jet lag
Cultural Judaism
Cultural lag
Cultural literacy
Cultural mosaic
Cultural movement
Cultural mulatto
Cultural Muslim
Cultural probe
Cultural relativism
Culture speculation
Cultural tourism
Pop-culture
Cultural translation
Cultural turn
Cultural sensibility
Culture and positive psychology
Culture and social cognition
Culture gap
Culture hero
Culture industry
Culture shock
Culturgen
Children's culture
Culturalism
Cyberculture
Death and culture
Disability culture
Deaf culture
Emotions and culture
Intercultural communication
Intercultural competence
Languaculture
Living things in culture
Media culture
Oppositional culture
Participatory culture
Permission culture
Rape culture
Remix culture
Tea culture
Transformation of culture
Urban culture
Welfare culture
Category
Portal
Commons
WikiProject
changes
Retrieved from "https://en.wikipedia.org/w/index.php?title=Conformity&oldid=830126668"
Categories:
Conformity
Community organizing
Group processes
Organizational behavior
Systems science
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Wikiquote
Languages
العربية
Asturianu
Azərbaycanca
Беларуская
Беларуская (тарашкевіца)
Български
Català
Čeština
Dansk
Deutsch
Español
فارسی
Français
한국어
Հայերեն
हिन्दी
Hrvatski
Bahasa Indonesia
Italiano
עברית
Кыргызча
Lietuvių
Magyar
Nederlands
日本語
Norsk
Norsk nynorsk
Polski
Português
Română
Русский
Slovenčina
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
Українська
中文
29 more
Edit links
This page was last edited on 12 March 2018, at 22:19.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

key: html

type: local

value: div

values: mw-page-base noprint

values: mw-head-base noprint

value: a

attrs: id class lang

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

attrs: href class title

values:
/wiki/Norm_(social)
mw-redirect
Norm (social)

values:
/wiki/Social_pressure
mw-redirect
Social pressure

value: p

attrs: href title

values: Edit section: Sherif's experiment (1936)

attrs: alt src width height class srcset data-file-width data-file-height

values:
/wiki/Social_psychology_(psychology)
mw-redirect
Social psychology (psychology)

values:
/wiki/Informational_social_influence
mw-redirect
Informational social influence

values:
/wiki/Ventral_striatum
mw-redirect
Ventral striatum

values: display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle

values: margin:0.5em 0 0.5em 1em;border:solid #aaa 1px

values: Propaganda: The Formation of Men's Attitudes

values:
nofollow
external text
//www.jstor.org/stable/1488401

values:
nofollow
external text
//doi.org/10.1037%2Fh0046408

values:
/wiki/PubMed_Identifier
mw-redirect
PubMed Identifier

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/13286010

values:
nofollow
external text
//doi.org/10.1037%2Fh0062326

values:
nofollow
external text
//doi.org/10.1207%2Fs15327957pspr1001_1

values:
nofollow
external text
//doi.org/10.2466%2Fpr0.1988.62.3.759

values:
nofollow
external text
//doi.org/10.1037%2Fh0025231

values:
nofollow
external text
//doi.org/10.1037%2Fh0046604

values:
nofollow
external text
//doi.org/10.1037%2Fh0041274

values:
nofollow
external text
//doi.org/10.1037%2Fh0030382

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/8758616

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/10224640

values:
nofollow
external text
//doi.org/10.1016%2Fj.conb.2013.03.009

values:
nofollow
external text
//doi.org/10.1016%2Fj.obhdp.2009.04.001

values:
nofollow
external text
//doi.org/10.1126%2Fscience.1203557

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/21719681

values:
nofollow
external text
//doi.org/10.3389%2Ffnhum.2013.00050

values:
nofollow
external text
//doi.org/10.3389%2Ffnhum.2012.00168

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/22701416

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/15978553

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/19879365

values:
nofollow
external text
//doi.org/10.3389%2Ffnhum.2010.00048

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/20589242

values:
nofollow
external text
//doi.org/10.1016%2Fj.cub.2012.01.012

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

values:
/wiki/Coercive_persuasion
mw-redirect
Coercive persuasion

values:
/wiki/Antisocial_tendencies
mw-redirect
Antisocial tendencies

values:
/wiki/Ritual_clown
mw-redirect
Ritual clown

values: nowraplinks collapsible autocollapse navbox-inner

values: navigation navbox Conformity padding:3px

values:
/wiki/Sound_culture
mw-redirect
Sound culture

values:
/wiki/Constructed_culture
mw-redirect
Constructed culture

values:
/wiki/Folk_culture
mw-redirect
Folk culture

values:
/wiki/High-_and_low-context_cultures
mw-redirect
High- and low-context cultures

values:
/wiki/Cultural_racism
mw-redirect
Cultural racism

values:
/wiki/Security_culture
mw-redirect
Security culture

values:
/wiki/Cultural_Mormon
mw-redirect
Cultural Mormon

values:
/wiki/Cultural_competence
mw-redirect
Cultural competence

values:
/wiki/Cultural_evolutionism
mw-redirect
Cultural evolutionism

values:
/wiki/Transformation_of_culture
mw-redirect
Transformation of culture

values: nowraplinks hlist collapsible collapsed navbox-inner

values:
catlinks mw-normal-catlinks
catlinks mw-normal-catlinks
interface

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Conformity
View the content page [ctrl-alt-c]
c

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values: امتثال (علم نفس) – Arabic

values:
interlanguage-link interwiki-ast
display: none;

values:
interlanguage-link interwiki-az
display: none;

values: Канфармізм – Belarusian

values:
interlanguage-link interwiki-be
display: none;

values: Канфармізм – Belarusian (Taraškievica orthography)

values:
interlanguage-link interwiki-be-x-old
display: none;

values: Конформизъм – Bulgarian

values:
interlanguage-link interwiki-bg
display: none;

values:
interlanguage-link interwiki-ca
display: none;

values:
interlanguage-link interwiki-cs
display: none;

values:
https://da.wikipedia.org/wiki/Konform
Konform – Danish
da
da
interlanguage-link-target

values:
interlanguage-link interwiki-da
display: none;

values: هم‌نوایی – Persian

values:
interlanguage-link interwiki-fa
display: none;

values:
interlanguage-link interwiki-ko
display: none;

values: Կոնֆորմիզմ – Armenian

values:
interlanguage-link interwiki-hy
display: none;

values: अनुरूपता – Hindi

values:
interlanguage-link interwiki-hr
display: none;

values:
interlanguage-link interwiki-it
display: none;

values: קונפורמיות – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values: Конформизм – Kyrgyz

values:
interlanguage-link interwiki-ky
display: none;

values:
interlanguage-link interwiki-lt
display: none;

values:
interlanguage-link interwiki-hu
display: none;

values:
interlanguage-link interwiki-nl
display: none;

values:
interlanguage-link interwiki-ja
display: none;

values:
interlanguage-link interwiki-no
display: none;

values:
interlanguage-link interwiki-nn
display: none;

values:
interlanguage-link interwiki-pl
display: none;

values:
interlanguage-link interwiki-ro
display: none;

values: Конформность – Russian

values:
interlanguage-link interwiki-sk
display: none;

values: Конформизам – Serbian

values:
interlanguage-link interwiki-sr
display: none;

values:
interlanguage-link interwiki-sh
display: none;

values:
interlanguage-link interwiki-fi
display: none;

values:
interlanguage-link interwiki-sv
display: none;

values: Конформізм – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values: All languages (initial selection from common choices by you and others)

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Conformity rootpage-Conformity skin-vector action-view


text:
Decimal
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
For other uses, see Decimal (disambiguation).
This article needs additional citations for verification. Relevant discussion may be found on the talk page. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2011) (Learn how and when to remove this template message)
Numeral systems
Hindu–Arabic numeral system
Western Arabic
Eastern Arabic
Bengali
Gurmukhi
Indian
Sinhala
Tamil
Balinese
Burmese
Dzongkha
Gujarati
Javanese
Khmer
Lao
Mongolian
Thai
East Asian
Chinese
Suzhou
Hokkien
Japanese
Korean
Vietnamese
Counting rods
Alphabetic
Abjad
Armenian
Āryabhaṭa
Cyrillic
Ge'ez
Georgian
Greek
Hebrew
Roman
Former
Aegean
Attic
Babylonian
Brahmi
Chuvash
Egyptian
Etruscan
Inuit
Kharosthi
Mayan
Muisca
Quipu
Prehistoric
Positional systems by base
2
3
4
5
6
8
10
12
16
20
60
Non-standard positional numeral systems
Bijective numeration (1)
Signed-digit representation (Balanced ternary)
factorial
negative
Complex-base system (2i)
Non-integer representation (φ)
mixed
Asymmetric numeral systems
List of numeral systems
v
t
e
The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system.[1] The way of denoting numbers in the decimal system is often referred to as Decimal notation.[2]
A decimal numeral, or just decimal, or, improperly decimal number, refers generally to the notation of a number in the decimal system, which contains a decimal separator (for example 10.00 or 3.14159). Sometimes these terms are used for any numeral in the decimal system. A decimal may also refer to any digit after the decimal separator, such as in "3.14 is the approximation of π to two decimals".
The numbers that may be represented in the decimal system are the decimal fractions, that is the fractions of the form a/10n, where a is an integer, and n is a nonnegative integer.
The decimal system has been extended to infinite decimals, for representing any real number, by using an infinite sequence of digits after the decimal separator (see Decimal representation). In this context, the usual decimals are sometimes called terminating decimals. A repeating decimal, is an infinite decimal, that, after some place repeats indefinitely the same sequence of digits (for example 5.123144144144144... = 5.123144).[3] An infinite decimal represents a rational number if and only if it is a repeating decimal or has a finite number of nonzero digits.
Contents
1 Origin
2 Decimal notation
3 Decimal fractions
4 Real number approximation
5 Infinite decimal expansion
5.1 Rational numbers
6 Decimal computation
7 History
7.1 History of decimal fractions
7.2 Natural languages
7.3 Other bases
8 See also
9 References
Origin[edit]
Ten fingers on two hands, the possible starting point of the decimal counting.
Many numeral systems of ancient civilisations use ten and its powers for representing numbers, probably because there are ten fingers on two hands and people started counting by using their fingers. Examples are Armenian numerals, Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals. Very large numbers were difficult to represent in these old numeral systems, and, only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called decimal fractions or decimal numbers for forming the decimal numeral system.
Decimal notation[edit]
For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−". The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;[4] the decimal separator is the dot "." in many countries (including English speaking ones), but may be a comma "," in other countries (mainly in Europe).
For representing a nonnegative number, a decimal consists of
either a (finite) sequence of digits such as 2017, or in full generality,
a m a m − 1 … a 0 {\displaystyle a_{m}a_{m-1}\ldots a_{0}}
(in this case, the (entire) decimal represents an integer)
or two sequence of digits separated by a decimal mark such as 3.14159, 15.00, or in full generality
a m a m − 1 … a 0 . b 1 b 2 … b n {\displaystyle a_{m}a_{m-1}\ldots a_{0}.b_{1}b_{2}\ldots b_{n}}
It is generally assumed that, if m > 0, the first digit am is not zero, but, in some circumstances, it may be useful to have one or more 0's on the left. This does not change the value represented by the decimal. For example, 3.14 = 03.14 = 003.14. Similarly, if bn =0, it may be removed, and conversely, trailing zeros may be added without changing the represented number. For example, 15 = 15.0 = 15.00 and 5.2 = 5.20 = 5.200. sometimes, the unnecessary zeros are used for indicating the accuracy of a measurement. For example, 15.00m may indicate that the measurement error is less than one centimeter, while 15m may mean that the length is roughly fifteen meters, and that the error may exceed 10 cm.
For representing a negative number, a minus sign is placed before am.
The numeral a m a m − 1 … a 0 . b 1 b 2 … b n {\displaystyle a_{m}a_{m-1}\ldots a_{0}.b_{1}b_{2}\ldots b_{n}} represents the number
a m 10 m + a m − 1 10 m − 1 + ⋯ + a 0 10 0 + b 1 10 1 + b 2 10 2 + ⋯ + b n 10 n {\displaystyle a_{m}10^{m}+a_{m-1}10^{m-1}+\cdots +a_{0}10^{0}+{\frac {b_{1}}{10^{1}}}+{\frac {b_{2}}{10^{2}}}+\cdots +{\frac {b_{n}}{10^{n}}}}
Therefore, the contribution of each digit to the value of a number depends on its position in the numeral. That is, the decimal system is a positional numeral system
Decimal fractions[edit]
The numbers that are represented by decimal numeral are the decimal fractions (sometimes called decimal numbers), that is, the rational numbers that may be expressed as a fraction, the denominator of which is a power of ten.[5] For example, the numerals 0.8 , 14.89 , 0.00024 {\displaystyle 0.8,14.89,0.00024} represent the fractions 8/10, 1489/100, 24/100000. More generally, a decimal with n digits after the separator represents the fraction with denominator 10n, whose numerator is the integer obtained by removing the separator.
Expressed as a fully reduced fraction, the decimal numbers are those, whose denominator is a product of a power of 2 by a power of 5. Thus the smallest denominators of decimal numbers are
1 = 2 0 ⋅ 5 0 , 2 = 2 1 ⋅ 5 0 , 4 = 2 2 ⋅ 5 0 , 5 = 2 0 ⋅ 5 1 , 8 = 2 3 ⋅ 5 0 , 10 = 2 1 ⋅ 5 1 , 16 = 2 4 ⋅ 5 0 , 25 = 2 0 ⋅ 5 2 , … {\displaystyle 1=2^{0}\cdot 5^{0},2=2^{1}\cdot 5^{0},4=2^{2}\cdot 5^{0},5=2^{0}\cdot 5^{1},8=2^{3}\cdot 5^{0},10=2^{1}\cdot 5^{1},16=2^{4}\cdot 5^{0},25=2^{0}\cdot 5^{2},\ldots }
The integer part, or integral part of a decimal is the integer written to the left of the decimal separator (see also truncation). For a nonnegative decimal, it is the largest integer that is not greater than the decimal. The part from the decimal separator to the right is the fractional part, which equals the difference between the numeral and its integer part.
When the integral part of a numeral is zero, it may occur, typically in computing, that the integer part is not written (for example .1234, instead of 0.1234). In normal writing, this is generally avoided because of the risk of confusion between the decimal mark and other punctuation.
Real number approximation[edit]
Decimal numerals do not allow an exact representation for all real numbers, so e.g. for the real number π. Nevertheless, they allow approximating every real number with any desired accuracy, e.g., the decimal 3.14159 approximates the real π, being less than 10−5 off; and so decimals are widely used in science, engineering and everyday life.
More precisely, for every real number x, and every positive integer n, there are two decimals l and u, with at most n digits after the decimal mark, such that l ≤ x ≤ u and (u – l) = 10−n.
Numbers are very often obtained as the result of a measurement. As measurements are generally afflicted with some measurement error with a known upper bound, the result of a measurement is well represented by a decimal with n digits after the decimal mark, as soon as the absolute measurement error is bounded from above by 10−n. In practice, measurement results are often given with a certain number of digits after the decimal point, which indicate the error bounds. For example, although 0.080 and 0.08 denote the same decimal number, the numeral 0.080 is to suggest a measurement with an error less than 0.001, while the numeral 0.08 indicates an absolute error bounded by 0.01. In both cases, the true value of the measured quantity could be, for example, 0.0803 or 0.0796 (see also significant figures).
Infinite decimal expansion[edit]
Main article: Decimal representation
For a real number x and an integer n ≥ 0, let [x]n denote the (finite) decimal expansion of the greatest number that is not greater than x, which has exactly n digits after the decimal mark. Let di denote the last digit of [x]i. It is straightforward to see that [x]n may be obtained by appending dn to the right of [x]n–1. This way one has
[x]n = [x]0.d1d2...dn−1dn,
and the difference of [x]n–1 and [x]n amounts to
|[x]n − [x]n–1| = dn ⋅ 10−n < 10−n+1,
which is either 0, if dn = 0, or gets arbitrarily small, when n tends to infinity. According to the definition of a limit, x is the limit of [x]n when n tends to infinity. This is written as x = lim n → ∞ [ x ] n {\textstyle \;x=\lim _{n\rightarrow \infty }[x]_{n}\;} or
x = [x]0.d1d2...dn...,
which is called an infinite decimal expansion of x.
Conversely, for any integer [x]0 and any sequence of digits ( d n ) n = 1 ∞ {\textstyle \;(d_{n})_{n=1}^{\infty }} the (infinite) expression [x]0.d1d2...dn... is an infinite decimal expansion of a real number x. This expansion is unique if neither all dn are equal to 9 nor all dn are equal to 0 for n large enough (for all n greater than some natural number N).
If all dn for n > N equal to 9 and [x]n = [x]0.d1d2...dn, the limit of the sequence ( [ x ] n ) n = 1 ∞ {\textstyle \;([x]_{n})_{n=1}^{\infty }} is the decimal fraction obtained by replacing the last digit that is not a 9, i.e.: dN, by dN + 1, and replacing all subsequent 9s by 0s (see 0.999...).
Any such decimal fraction, i.e., dn = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing dN by dN − 1, and replacing all subsequent 0s by 9s (see 0.999...).
In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion. Each decimal fraction has exactly two infinite decimal expansions, one containing only 0s after some place, which is obtained by the above definition of [x]n, and the other containing only 9s after some place, which is obtained by defining [x]n as the greatest number that is less than x, having exactly n digits after the decimal mark.
Rational numbers[edit]
Main article: Repeating decimal
The long division allows computing the infinite decimal expansion of a rational number. If the rational number is a decimal fraction, the division stops eventually, producing a decimal numeral, which may be prolongated into an infinite expansion by adding infinitely many 0. If the rational number is not a decimal fraction, the division may continue indefinitely. However, as all successive remainder are less than the divisor, there are only a finite number of possible remainders, and after some place, the same sequence of digits must be repeated indefinitely in the quotient. That is, one has a repeating decimal. For example,
1/81 = 0. 012345679 012... (with the group 012345679 indefinitely repeating).
Conversely, every eventually repeating sequence of digit is the infinite decimal expansion of a rational number. This is a consequence of the fact that the recurring part of a decimal representation is, in fact, an infinite geometric series which will sum to a rational number. For example,
0.0123123123 … = 123 10000 ∑ k = 0 ∞ 0.001 k = 123 10000 1 1 − 0.001 = 123 9990 = 41 3330 {\displaystyle 0.0123123123\ldots ={\frac {123}{10000}}\sum _{k=0}^{\infty }0.001^{k}={\frac {123}{10000}}\ {\frac {1}{1-0.001}}={\frac {123}{9990}}={\frac {41}{3330}}}
Decimal computation[edit]
Diagram of the world's earliest multiplication table (c. 305 BC) from the Warring States period
Modern computer hardware and software systems commonly use a binary representation internally (although many early computers, such as the ENIAC or the IBM 650, used decimal representation internally).[6] For external use by computer specialists, this binary representation is sometimes presented in the related octal or hexadecimal systems.
For most purposes, however, binary values are converted to or from the equivalent decimal values for presentation to or input from humans; computer programs express literals in decimal by default. (123.1, for example, is written as such in a computer program, even though many computer languages are unable to encode that number precisely.)
Both computer hardware and software also use internal representations which are effectively decimal for storing decimal values and doing arithmetic. Often this arithmetic is done on data which are encoded using some variant of binary-coded decimal,[7][8] especially in database implementations, but there are other decimal representations in use (such as in the new IEEE 754 Standard for Floating-Point Arithmetic).[9]
Decimal arithmetic is used in computers so that decimal fractional results of adding (or subtracting) values with a fixed length of their fractional part always are computed to this same length of precision. This is especially important for financial calculations, e.g., requiring in their results integer multiples of the smallest currency unit for book keeping purposes. This is not possible in binary, because the negative powers of 10 {\displaystyle 10} have no finite binary fractional representation; and is generally impossible for multiplication (or division).[10][11] See Arbitrary-precision arithmetic for exact calculations.
History[edit]
The world's earliest decimal multiplication table was made from bamboo slips, dating from 305 BC, during the Warring States period in China.
Many ancient cultures calculated with numerals based on ten, sometimes argued due to human hands typically having ten digits.[12] Standardized weights used in Indus Valley Civilization (c.3300-1300 BCE) were based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, while their standardized ruler – the Mohenjo-daro ruler – was divided into ten equal parts.[13][14][15] Egyptian hieroglyphs, in evidence since around 3000 BC, used a purely decimal system,[16] just as the Cretan hieroglyphs (ca. 1625−1500 BC) of the Minoans whose numerals are closely based on the Egyptian model.[17][18] The decimal system was handed down to the consecutive Bronze Age cultures of Greece, including Linear A (ca. 18th century BC−1450 BC) and Linear B (ca. 1375−1200 BC) — the number system of classical Greece also used powers of ten, including, like the Roman numerals did, an intermediate base of 5.[19] Notably, the polymath Archimedes (ca. 287–212 BC) invented a decimal positional system in his Sand Reckoner which was based on 108[19] and later led the German mathematician Carl Friedrich Gauss to lament what heights science would have already reached in his days if Archimedes had fully realized the potential of his ingenious discovery.[20] The Hittites hieroglyphs (since 15th century BC), just like the Egyptian and early numerals in Greece, was strictly decimal.[21]
Some non-mathematical ancient texts like the Vedas dating back to 1900–1700 BCE make use of decimals and mathematical decimal fractions.[22]
The Egyptian hieratic numerals, the Greek alphabet numerals, the Hebrew alphabet numerals, the Roman numerals, the Chinese numerals and early Indian Brahmi numerals are all non-positional decimal systems, and required large numbers of symbols. For instance, Egyptian numerals used different symbols for 10, 20, to 90, 100, 200, to 900, 1000, 2000, 3000, 4000, to 10,000.[23] The world's earliest positional decimal system was the Chinese rod calculus.[24]
The world's earliest positional decimal system
Upper row vertical form
Lower row horizontal form
History of decimal fractions[edit]
counting rod decimal fraction 1/7
Decimal fractions were first developed and used by the Chinese in the end of 4th century BC,[25] and then spread to the Middle East and from there to Europe.[24][26] The written Chinese decimal fractions were non-positional.[26] However, counting rod fractions were positional.[24]
Qin Jiushao in his book Mathematical Treatise in Nine Sections (1247[27]) denoted 0.96644 by
寸
, meaning
寸
096644
J. Lennart Berggren notes that positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century.[28] The Jewish mathematician Immanuel Bonfils used decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them.[29] The Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century.[28] Al Khwarizmi introduced fraction to Islamic countries in the early 9th century, his fraction presentation was an exact copy of traditional Chinese mathematical fraction from Sunzi Suanjing.[24] This form of fraction with numerator on top and denominator at bottom without a horizontal bar was also used by 10th century Abu'l-Hasan al-Uqlidisi and 15th century Jamshīd al-Kāshī's work "Arithmetic Key".[24][30]
A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century.[31]
Natural languages[edit]
The ingenious method of expressing every possible number using a set of ten symbols emerged in India. Several Indian languages show a straightforward decimal system. Many Indo-Aryan and Dravidian languages have numbers between 10 and 20 expressed in a regular pattern of addition to 10.[32]
The Hungarian language also uses a straightforward decimal system. All numbers between 10 and 20 are formed regularly (e.g. 11 is expressed as "tizenegy" literally "one on ten"), as with those between 20 and 100 (23 as "huszonhárom" = "three on twenty").
A straightforward decimal rank system with a word for each order (10 十, 100 百, 1000 千, 10,000 万), and in which 11 is expressed as ten-one and 23 as two-ten-three, and 89,345 is expressed as 8 (ten thousands) 万 9 (thousand) 千 3 (hundred) 百 4 (tens) 十 5 is found in Chinese, and in Vietnamese with a few irregularities. Japanese, Korean, and Thai have imported the Chinese decimal system. Many other languages with a decimal system have special words for the numbers between 10 and 20, and decades. For example, in English 11 is "eleven" not "ten-one" or "one-teen".
Incan languages such as Quechua and Aymara have an almost straightforward decimal system, in which 11 is expressed as ten with one and 23 as two-ten with three.
Some psychologists suggest irregularities of the English names of numerals may hinder children's counting ability.[33]
Other bases[edit]
Main article: positional notation
Units of
information
shannon or bit (base 2)
nat (base e)
trit (base 3)
hartley, ban or dit (base 10)
qubit (quantum)
v
t
e
Some cultures do, or did, use other bases of numbers.
Pre-Columbian Mesoamerican cultures such as the Maya used a base-20 system (perhaps based on using all twenty fingers and toes).
The Yuki language in California and the Pamean languages[34] in Mexico have octal (base-8) systems because the speakers count using the spaces between their fingers rather than the fingers themselves.[35]
The existence of a non-decimal base in the earliest traces of the Germanic languages, is attested by the presence of words and glosses meaning that the count is in decimal (cognates to ten-count or tenty-wise), such would be expected if normal counting is not decimal, and unusual if it were.[36][37] Where this counting system is known, it is based on the long hundred of 120 in number, and a long thousand of 1200 in number. The descriptions like 'long' only appear after the small hundred of 100 in number appeared with the Christians. Gordon's Introduction to Old Norse p 293, gives number names that belong to this system. An expression cognate to 'one hundred and eighty' is translated to 200, and the cognate to 'two hundred' is translated at 240. Goodare details the use of the long hundred in Scotland in the Middle Ages, giving examples, calculations where the carry implies i C (i.e. one hundred) as 120, etc. That the general population were not alarmed to encounter such numbers suggests common enough use. It is also possible to avoid hundred-like numbers by using intermediate units, such as stones and pounds, rather than a long count of pounds. Goodare gives examples of numbers like vii score, where one avoids the hundred by using extended scores. There is also a paper by W.H. Stevenson, on 'Long Hundred and its uses in England'.[citation needed]
Many or all of the Chumashan languages originally used a base-4 counting system, in which the names for numbers were structured according to multiples of 4 and 16.[38]
Many languages[39] use quinary (base-5) number systems, including Gumatj, Nunggubuyu,[40] Kuurn Kopan Noot[41] and Saraveca. Of these, Gumatj is the only true 5–25 language known, in which 25 is the higher group of 5.
Some Nigerians use duodecimal systems.[42] So did some small communities in India and Nepal, as indicated by their languages.[43]
The Huli language of Papua New Guinea is reported to have base-15 numbers.[44] Ngui means 15, ngui ki means 15 × 2 = 30, and ngui ngui means 15 × 15 = 225.
Umbu-Ungu, also known as Kakoli, is reported to have base-24 numbers.[45] Tokapu means 24, tokapu talu means 24 × 2 = 48, and tokapu tokapu means 24 × 24 = 576.
Ngiti is reported to have a base-32 number system with base-4 cycles.[39]
The Ndom language of Papua New Guinea is reported to have base-6 numerals.[46] Mer means 6, mer an thef means 6 × 2 = 12, nif means 36, and nif thef means 36×2 = 72.
See also[edit]
Algorism
Binary-coded decimal (BCD)
Decimal computer
Decimal representation
Decimal separator
Densely packed decimal (DPD)
Dewey Decimal Classification (DDC)
Duodecimal
Octal
Scientific notation
SI prefix
References[edit]
Jump up ^ The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
Jump up ^ Lam Lay Yong & Ang Tian Se (2004) Fleeting Footsteps. Tracing the Conception of Arithmetic and Algebra in Ancient China, Revised Edition, World Scientific, Singapore.
Jump up ^ The viniculum (overline) in 5.123144 indicates that the '144' sequence repeats itself indefinitely, i.e. 7000512314414414414♠5.123144144144144....
Jump up ^ In some countries, such as Arab speaking ones, other glyphs are used for the digits
Jump up ^ "Decimal Fraction". Encyclopedia of Mathematics. Retrieved 2013-06-18.
Jump up ^ Fingers or Fists? (The Choice of Decimal or Binary Representation), Werner Buchholz, Communications of the ACM, Vol. 2 #12, pp3–11, ACM Press, December 1959.
Jump up ^ Schmid, Hermann (1983) [1974]. Decimal Computation (1 (reprint) ed.). Malabar, Florida, USA: Robert E. Krieger Publishing Company. ISBN 0-89874-318-4.
Jump up ^ Schmid, Hermann (1974). Decimal Computation (1st ed.). Binghamton, New York, USA: John Wiley & Sons. ISBN 0-471-76180-X.
Jump up ^ Decimal Floating-Point: Algorism for Computers, Cowlishaw, M. F., Proceedings 16th IEEE Symposium on Computer Arithmetic, ISBN 0-7695-1894-X, pp104-111, IEEE Comp. Soc., June 2003
Jump up ^ Decimal Arithmetic – FAQ
Jump up ^ Decimal Floating-Point: Algorism for Computers, Cowlishaw, M. F., Proceedings 16th IEEE Symposium on Computer Arithmetic (ARITH 16), ISBN 0-7695-1894-X, pp. 104–111, IEEE Comp. Soc., June 2003
Jump up ^ Dantzig, Tobias (1954), Number / The Language of Science (4th ed.), The Free Press (Macmillan Publishing Co.), p. 12, ISBN 0-02-906990-4
Jump up ^ Sergent, Bernard (1997), Genèse de l'Inde (in French), Paris: Payot, p. 113, ISBN 2-228-89116-9
Jump up ^ Coppa, A.; et al. (6 April 2006), "Early Neolithic tradition of dentistry: Flint tips were surprisingly effective for drilling tooth enamel in a prehistoric population" (PDF), Nature, 440 (7085): 755–6, Bibcode:2006Natur.440..755C, doi:10.1038/440755a, PMID 16598247
Jump up ^ Bisht, R. S. (1982), "Excavations at Banawali: 1974–77", in Possehl, Gregory L. (ed.), Harappan Civilisation: A Contemporary Perspective, New Delhi: Oxford and IBH Publishing Co., pp. 113–124
Jump up ^ Georges Ifrah: From One to Zero. A Universal History of Numbers, Penguin Books, 1988, ISBN 0-14-009919-0, pp. 200–213 (Egyptian Numerals)
Jump up ^ Graham Flegg: Numbers: their history and meaning, Courier Dover Publications, 2002, ISBN 978-0-486-42165-0, p. 50
Jump up ^ Georges Ifrah: From One to Zero. A Universal History of Numbers, Penguin Books, 1988, ISBN 0-14-009919-0, pp. 213–218 (Cretan numerals)
^ Jump up to: a b Greek numerals
Jump up ^ Menninger, Karl: Zahlwort und Ziffer. Eine Kulturgeschichte der Zahl, Vandenhoeck und Ruprecht, 3rd. ed., 1979, ISBN 3-525-40725-4, pp. 150–153
Jump up ^ Georges Ifrah: From One to Zero. A Universal History of Numbers, Penguin Books, 1988, ISBN 0-14-009919-0, pp. 218f. (The Hittite hieroglyphic system)
Jump up ^ (Atharva Veda 5.15, 1-11)
Jump up ^ Lam Lay Yong et al. The Fleeting Footsteps pp 137–139
^ Jump up to: a b c d e Lam Lay Yong, "The Development of Hindu–Arabic and Traditional Chinese Arithmetic", Chinese Science, 1996 p38, Kurt Vogel notation
Jump up ^ "Ancient bamboo slips for calculation enter world records boo". The Institute of Archaeology, Chinese Academy of Social Sciences. Retrieved 10 May 2017.
^ Jump up to: a b Joseph Needham (1959). "Decimal System". Science and Civilisation in China, Volume III, Mathematics and the Sciences of the Heavens and the Earth. Cambridge University Press.
Jump up ^ Jean-Claude Martzloff, A History of Chinese Mathematics, Springer 1997 ISBN 3-540-33782-2
^ Jump up to: a b Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". In Katz, Victor J. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 530. ISBN 978-0-691-11485-9.
Jump up ^ Gandz, S.: The invention of the decimal fractions and the application of the exponential calculus by Immanuel Bonfils of Tarascon (c. 1350), Isis 25 (1936), 16–45.
Jump up ^ Lam Lay Yong, "A Chinese Genesis, Rewriting the history of our numeral system", Archive for History of Exact Science 38: 101–108.
Jump up ^ B. L. van der Waerden (1985). A History of Algebra. From Khwarizmi to Emmy Noether. Berlin: Springer-Verlag.
Jump up ^ "Indian numerals". Ancient Indian mathematics. Retrieved 2015-05-22.
Jump up ^ Azar, Beth (1999). "English words may hinder math skills development". American Psychology Association Monitor. 30 (4). Archived from the original on 2007-10-21.
Jump up ^ Avelino, Heriberto (2006). "The typology of Pame number systems and the limits of Mesoamerica as a linguistic area" (PDF). Linguistic Typology. 10 (1): 41–60. doi:10.1515/LINGTY.2006.002.
Jump up ^ Marcia Ascher. "Ethnomathematics: A Multicultural View of Mathematical Ideas". The College Mathematics Journal. JSTOR 2686959.
Jump up ^ McClean, R. J. (July 1958), "Observations on the Germanic numerals", German Life and Letters, 11 (4): 293–299, doi:10.1111/j.1468-0483.1958.tb00018.x, Some of the Germanic languages appear to show traces of an ancient blending of the decimal with the vigesimal system .
Jump up ^ Voyles, Joseph (October 1987), "The cardinal numerals in pre-and proto-Germanic", The Journal of English and Germanic Philology, 86 (4): 487–495, JSTOR 27709904 .
Jump up ^ There is a surviving list of Ventureño language number words up to 32 written down by a Spanish priest ca. 1819. "Chumashan Numerals" by Madison S. Beeler, in Native American Mathematics, edited by Michael P. Closs (1986), ISBN 0-292-75531-7.
^ Jump up to: a b Hammarström, Harald (17 May 2007). "Rarities in Numeral Systems". In Wohlgemuth, Jan; Cysouw, Michael. Rethinking Universals: How rarities affect linguistic theory (PDF). Empirical Approaches to Language Typology. 45. Berlin: Mouton de Gruyter (published 2010). Archived from the original (PDF) on 19 August 2007.
Jump up ^ Harris, John (1982). Hargrave, Susanne, ed. Facts and fallacies of aboriginal number systems (PDF). Work Papers of SIL-AAB Series B. 8. pp. 153–181. Archived from the original (PDF) on 2007-08-31.
Jump up ^ Dawson, J. "Australian Aborigines: The Languages and Customs of Several Tribes of Aborigines in the Western District of Victoria (1881), p. xcviii.
Jump up ^ Matsushita, Shuji (1998). Decimal vs. Duodecimal: An interaction between two systems of numeration. 2nd Meeting of the AFLANG, October 1998, Tokyo. Archived from the original on 2008-10-05. Retrieved 2011-05-29.
Jump up ^ Mazaudon, Martine (2002). "Les principes de construction du nombre dans les langues tibéto-birmanes". In François, Jacques. La Pluralité (PDF). Leuven: Peeters. pp. 91–119. ISBN 90-429-1295-2
Jump up ^ Cheetham, Brian (1978). "Counting and Number in Huli". Papua New Guinea Journal of Education. 14: 16–35. Archived from the original on 2007-09-28.
Jump up ^ Bowers, Nancy; Lepi, Pundia (1975). "Kaugel Valley systems of reckoning" (PDF). Journal of the Polynesian Society. 84 (3): 309–324. Archived from the original (PDF) on 2011-06-04.
Jump up ^ Owens, Kay (2001), "The Work of Glendon Lean on the Counting Systems of Papua New Guinea and Oceania", Mathematics Education Research Journal, 13 (1): 47–71, doi:10.1007/BF03217098, archived from the original on 2015-09-26
Authority control
GND: 4149429-5
Retrieved from "https://en.wikipedia.org/w/index.php?title=Decimal&oldid=865416447"
Categories:
Elementary arithmetic
Fractions (mathematics)
Positional numeral systems
Hidden categories:
Articles with inconsistent citation formats
Articles needing additional references from January 2011
All articles needing additional references
Articles containing Chinese-language text
All articles with unsourced statements
Articles with unsourced statements from June 2013
Wikipedia articles with GND identifiers
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
العربية
Asturianu
Azərbaycanca
বাংলা
Bân-lâm-gú
Беларуская
Беларуская (тарашкевіца)
Български
Bosanski
Brezhoneg
Català
Čeština
ChiShona
Cymraeg
Deutsch
Eesti
Ελληνικά
Español
Esperanto
Euskara
فارسی
Français
Gaeilge
Galego
한국어
Հայերեն
हिन्दी
Hrvatski
Bahasa Indonesia
IsiXhosa
Íslenska
Italiano
עברית
Basa Jawa
ಕನ್ನಡ
Қазақша
Kreyòl ayisyen
Latina
Latviešu
Magyar
Македонски
മലയാളം
Bahasa Melayu
Mirandés
Монгол
Nederlands
日本語
Norsk
Norsk nynorsk
Occitan
Олык марий
ਪੰਜਾਬੀ
Polski
Português
Română
Runa Simi
Русский
Sesotho sa Leboa
Simple English
Slovenčina
Slovenščina
کوردی
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
தமிழ்
ไทย
Українська
اردو
Tiếng Việt
文言
吴语
ייִדיש
粵語
中文
Lingua Franca Nova
68 more
Edit links
This page was last edited on 23 October 2018, at 20:20 (UTC).
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

attrs: id class

values: mw-page-base noprint

values: mw-head-base noprint

values: firstHeading firstHeading en

values: siteSub noprint

attrs: class href

values: mw-jump-link #mw-head

values: mw-jump-link #p-search

values:
/wiki/Decimal_(disambiguation)
mw-disambig
Decimal (disambiguation)

attrs: role class

values:
note
hatnote navigation-not-searchable

value: img

attrs: alt src width height srcset data-file-width data-file-height

attrs: href class

value: td

value: b

values: Help:Introduction to referencing with Wiki Markup/1

value: span

value: i

value: small

values: plainlinks metadata ambox ambox-content ambox-Refimprove

values:
/wiki/Bengali%E2%80%93Assamese_numerals
mw-redirect
Bengali–Assamese numerals

values:
/wiki/Kharosthi_numerals
mw-redirect
Kharosthi numerals

values: padding:0.3em 0.4em 0.3em;font-weight:bold;border-top:1px solid #aaa;border-bottom:1px solid #aaa;

values: vertical-navbox nowraplinks navbox hlist

values: float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%

values:
/wiki/10_(number)
mw-redirect
10 (number)

values:
/wiki/Positional_numeral_system
mw-redirect
Positional numeral system

values:
/wiki/Decimal_mark
mw-redirect
Decimal mark

values:
/wiki/Nonnegative_integer
mw-redirect
Nonnegative integer

values:
/wiki/Sequence_(mathematics)
mw-redirect
Sequence (mathematics)

values: checkbox button toctogglecheckbox toctogglecheckbox display:none

values:
/wiki/Decimal_digit
mw-redirect
Decimal digit

values:
/wiki/Nonnegative_number
mw-redirect
Nonnegative number

values: vertical-align: -0.671ex; width:13.692ex; height:2.009ex;

values: vertical-align: -0.671ex; width:24.543ex; height:2.509ex;

values: vertical-align: -2.338ex; width:61.813ex; height:5.843ex;

values: vertical-align: -0.671ex; width:17.958ex; height:2.509ex;

values: display:block; line-height:1em; margin:0 0.1em;

values: display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;

values: display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;

values:
/wiki/Fully_reduced_fraction
mw-redirect
Fully reduced fraction

values: vertical-align: -0.671ex; width:97.469ex; height:3.009ex;

values:
/wiki/Integer_part
mw-redirect
Integer part

values:
/wiki/Measurement_error
mw-redirect
Measurement error

values:
/wiki/Upper_bound
mw-redirect
Upper bound

values: Edit section: Infinite decimal expansion

values: vertical-align: -0.838ex; width:17.295ex; height:2.843ex;

values: vertical-align: -1.005ex; width:8.201ex; height:3.009ex;

values: vertical-align: -1.005ex; width:9.615ex; height:3.009ex;

values: vertical-align: -3.171ex; width:74.438ex; height:7.009ex;

values:
/wiki/Binary_numeral_system
mw-redirect
Binary numeral system

values: vertical-align: -0.338ex; width:2.325ex; height:2.176ex;

values:
/wiki/Warring_States
mw-redirect
Warring States

values:
/wiki/Indus_Valley_Civilization
mw-redirect
Indus Valley Civilization

values:
/wiki/Bronze_Age_Greece
mw-redirect
Bronze Age Greece

values: Edit section: History of decimal fractions

attrs: alt src width height data-file-width data-file-height

values:
/wiki/Al_Khwarizmi
mw-redirect
Al Khwarizmi

values:
/wiki/Quechua_languages
mw-redirect
Quechua languages

values:
/wiki/Units_of_measurement
mw-redirect
Units of measurement

values: padding:0.3em 0.4em 0.3em;font-weight:bold;background:lavender; font-size:120%;

values:
/wiki/Trit_(computing)
mw-redirect
Trit (computing)

values:
/wiki/Ternary_number
mw-redirect
Ternary number

values:
/wiki/Ban_(information)
mw-redirect
Ban (information)

values:
/wiki/Dit_(information)
mw-redirect
Dit (information)

values: float:right;clear:right;width:auto;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%

values: This claim needs references to reliable sources. (June 2013)

values:
noprint Inline-Template Template-Fact
white-space:nowrap;

values:
/wiki/Gumatj_language
mw-redirect
Gumatj language

values:
/wiki/Umbu-Ungu_language
mw-redirect
Umbu-Ungu language

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em;

values:
/wiki/Arab_language
mw-redirect
Arab language

values: 16th IEEE Symposium on Computer Arithmetic

values:
nofollow
http://www.dec.usc.es/arith16/
external text

values:
/wiki/PubMed_Identifier
mw-redirect
PubMed Identifier

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/16598247

values:
nofollow
external text
//doi.org/10.1515%2FLINGTY.2006.002

values:
nofollow
external text
//www.jstor.org/stable/2686959

values:
nofollow
external text
//www.jstor.org/stable/27709904

values:
nofollow
external text
//doi.org/10.1007%2FBF03217098

attrs: alt src width height style srcset data-file-width data-file-height

values:
nofollow
external text
https://d-nb.info/gnd/4149429-5

values: Category:Articles with inconsistent citation formats

values: Category:Articles needing additional references from January 2011

values: Category:All articles needing additional references

values: Category:Articles containing Chinese-language text

values: Category:All articles with unsourced statements

values: Category:Articles with unsourced statements from June 2013

values: Category:Wikipedia articles with GND identifiers

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Decimal
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values:
/w/index.php?title=Decimal&action=edit
Edit this page [ctrl-alt-e]
e

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values: نظام عد عشري – Arabic

values: Sistema de numberación decimal – Asturian

values:
interlanguage-link interwiki-ast
display: none;

values:
interlanguage-link interwiki-az
display: none;

values: দশমিক পদ্ধতি – Bangla

values:
interlanguage-link interwiki-bn
display: none;

values:
interlanguage-link interwiki-zh-min-nan
display: none;

values: Дзесятковая сістэма злічэння – Belarusian

values:
interlanguage-link interwiki-be
display: none;

values: Дзесятковая сыстэма зьлічэньня – Belarusian (Taraškievica orthography)

values:
interlanguage-link interwiki-be-x-old
display: none;

values: Десетична бройна система – Bulgarian

values:
interlanguage-link interwiki-bg
display: none;

values:
interlanguage-link interwiki-bs
display: none;

values:
interlanguage-link interwiki-br
display: none;

values:
interlanguage-link interwiki-ca
display: none;

values:
interlanguage-link interwiki-cs
display: none;

values:
interlanguage-link interwiki-sn
display: none;

values:
https://cy.wikipedia.org/wiki/Degol
Degol – Welsh
cy
cy
interlanguage-link-target

values:
interlanguage-link interwiki-cy
display: none;

values:
interlanguage-link interwiki-de
display: none;

values:
interlanguage-link interwiki-et
display: none;

values: Δεκαδικό σύστημα – Greek

values:
interlanguage-link interwiki-el
display: none;

values:
interlanguage-link interwiki-eo
display: none;

values:
interlanguage-link interwiki-eu
display: none;

values:
interlanguage-link interwiki-fa
display: none;

values:
interlanguage-link interwiki-fr
display: none;

values:
interlanguage-link interwiki-ga
display: none;

values: Sistema de numeración decimal – Galician

values:
interlanguage-link interwiki-gl
display: none;

values:
interlanguage-link interwiki-ko
display: none;

values: Տասնորդական հաշվման համակարգեր – Armenian

values:
interlanguage-link interwiki-hy
display: none;

values: दशमलव पद्धति – Hindi

values:
interlanguage-link interwiki-hr
display: none;

values:
https://xh.wikipedia.org/wiki/I-decimal
I-decimal – Xhosa
xh
xh
interlanguage-link-target

values:
interlanguage-link interwiki-xh
display: none;

values:
https://is.wikipedia.org/wiki/Tugakerfi
Tugakerfi – Icelandic
is
is
interlanguage-link-target

values:
interlanguage-link interwiki-is
display: none;

values:
interlanguage-link interwiki-it
display: none;

values: השיטה העשרונית – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values:
interlanguage-link interwiki-jv
display: none;

values: ದಶಮಾನ ಪದ್ಧತಿ – Kannada

values:
interlanguage-link interwiki-kn
display: none;

values: Сандардың ондық жүйесі – Kazakh

values:
interlanguage-link interwiki-kk
display: none;

values:
interlanguage-link interwiki-ht
display: none;

values:
interlanguage-link interwiki-la
display: none;

values:
interlanguage-link interwiki-lv
display: none;

values:
interlanguage-link interwiki-hu
display: none;

values: Десетичен броен систем – Macedonian

values:
interlanguage-link interwiki-mk
display: none;

values: ദശാംശ സമ്പ്രദായം – Malayalam

values:
interlanguage-link interwiki-ml
display: none;

values: Sistema de numeraçon decimal – Mirandese

values:
interlanguage-link interwiki-mwl
display: none;

values: Аравтын тооллын систем – Mongolian

values:
interlanguage-link interwiki-mn
display: none;

values:
interlanguage-link interwiki-nl
display: none;

values:
interlanguage-link interwiki-oc
display: none;

values: Луан чотрадам системе – Eastern Mari

values:
interlanguage-link interwiki-mhr
display: none;

values: ਇਸ਼ਾਰੀਆ – Punjabi

values:
interlanguage-link interwiki-pa
display: none;

values: Sistema de numeração decimal – Portuguese

values:
interlanguage-link interwiki-qu
display: none;

values: Десятичная система счисления – Russian

values:
interlanguage-link interwiki-nso
display: none;

values:
interlanguage-link interwiki-simple
display: none;

values:
interlanguage-link interwiki-sl
display: none;

values: نواندنی دەدەیی – Central Kurdish

values:
interlanguage-link interwiki-ckb
display: none;

values: Декадни систем – Serbian

values: பதின்மம் – Tamil

values:
interlanguage-link interwiki-ta
display: none;

values: เลขฐานสิบ – Thai

values:
interlanguage-link interwiki-th
display: none;

values: Десяткова система числення – Ukrainian

values: معید اعشاریہ – Urdu

values:
interlanguage-link interwiki-vi
display: none;

values:
interlanguage-link interwiki-wuu
display: none;

values: דעצימאל – Yiddish

values:
interlanguage-link interwiki-yi
display: none;

values:
interlanguage-link interwiki-zh-yue
display: none;

values:
interlanguage-link interwiki-lfn
display: none;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Decimal rootpage-Decimal skin-vector action-view