Question

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$
$0.\overline{6}$

Answer 1

Let $x=0.\overline{6}$

$10x=6.\overline{6}$

$10x=6+x$

$9x=6$

$x=\frac{6}{9}\Rightarrow x=\frac{2}{3}$