Question

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

$\mathrm{0.888...}$ is $\frac{8}{m}$, then $m$ is equal to

Answer 1

Let $x$ be $\mathrm{0.888...}$
$=>10x=\mathrm{8.888...}$
$=>10x=8+\mathrm{0.888..}$
$=>10x=8+x$
$=>10x-x=8$
$=>9x=8$
$=>x=\frac{8}{9}$

Hence, $m=9$