[tex]1.6666...=1.\overline{6}=1.(6)\\\\x=1.6666...\ \ \ |multiply\ both\ sides\ by\ 10\\10x=16.6666...\\\\10x-x=16.6666...-1.6666...\\9x=15\ \ \ \ |divide\ both\ sides\ by\ 9\\\\x=\frac{15}{9}\\\\\boxed{x=1\frac{6}{9}}\\\\simplify\\\\x=1\frac{6:3}{9:3}=\boxed{1\frac{2}{3}}[/tex]