Question

Express in $\frac{p}{q}$ form
$0.\overline{6}$

Answer 1

Let $x=0.\overline{6}.............\left(1\right)10x=6.\overline{6}..............\left(2\right)$

Subtracting (1) from (2)

$10x-x=6.\overline{6}-0.\overline{6}\Rightarrow 9x=6\Rightarrow x=\frac{6}{9}=\frac{2}{3}$