Question

Express $5.\overline{2}$ in the form of $\frac{p}{q},$ where $p$ and $q$ are integers and

Answer 1

$5.\overline{2}$ in $\frac{p}{q}$ form
let $x=5.222....-\left(1\right)$
Multiply both side by 10,
$10x=52.222.....-\left(2\right)$
Subtract $\left(2\right)$ from $\left(1\right),$
$9x=47$
$x=\frac{47}{9}$