Question

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

Answer 1

$0.\overline{6}$ = 0.666...

Let x = 0.666...
$\Rightarrow$ 10x = 6.666... [Since only one digit is repeating, so multiply x with 10.]
$\Rightarrow$ 10x = 6 + .666...
$\Rightarrow$ 10x = 6 + x
$\Rightarrow$ 9x = 6
$\Rightarrow$ $x=\frac{2}{3}$