[tex]x=0.1666...\ \ \ \ |multiply\ both\ sides\ by\ 10\\\\10x=1.666...\ \ \ |multiply\ both\ sides\ by\ 10\\\\100x=16.666....\\\\100x-10x=16.666...-1.666...\\\\90x=15\ \ \ \ |divide\ both\ sides\ by\ 90\\\\x=\dfrac{15}{90}\\\\x=\dfrac{1}{6}\\\\\\Answer:\boxed{0.1666...=\frac{1}{6}}[/tex]
