[tex]x=1.121212...\ \ \ \ \ |multiply\ both\ sides\ by\ 100\\\\100x=112.121212...\\\\100x-x=112.121212...-1.121212...\\\\99x=111\ \ \ \ |divide\ both\ sides\ by\ 99\\\\x=\dfrac{111:3}{99:3}\\\\x=\dfrac{37}{33}\\\\x=1\dfrac{4}{33}\\\\Answer:\boxed{1.121212...=1\frac{4}{33}}[/tex]
