0.1(50)=5\\-------------------\\if\ 0.1(50)=0.1505050...\ then:\\\\x=0.1(50)\ \ \ \ |multiply\ both\ sides\ by\ 10\\\\10x=1.(50)\ \ \ \ |multiply\ both\ sides\ by\ 100\\\\1000x=150.(50)\\\\1000x-10x=150.(50)-1.(50)\\\\990x=149\ \ \ \ \ \ |divide\ both\ sides\ by\ 990\\\\\boxed{x=\frac{149}{990}}