Question

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

$5.\overline{2}$ is $\frac{47}{m}$, then $m$ is

Answer 1

Let $x$ be $5.222\dots$
$\Rightarrow 10x=52.222\dots$
$\Rightarrow 10x=47+5.222\dots$
$\Rightarrow 10x=47+x$
$\Rightarrow 10x-x=47$
$\Rightarrow 9x=47$
$\Rightarrow x=\frac{47}{9}$

Thus in the given question, the value of $m$ is $9.$