[tex]0.\overline{282}=0.282282282...\\\\x=0.282282282...\ \ \ \ \ \ |multiply\ both\ sides\ by\ 1000\\\\1000x=282.282282282...\\\\1000x-x=282.282282282...-0.282282282...\\\\999x=282\ \ \ \ \ |divide\ both\ sides\ by\ 999\\\\x=\dfrac{282}{999}\\\\x=\dfrac{282:3}{999:3}\\\\x=\dfrac{94}{333}\\\\Answer:\boxed{0.\overline{282}=\frac{94}{333}}[/tex]
