Question

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

$\mathrm{0.2555...}$ is $\frac{23}{m}$, then $m$ is equal to

Answer 1

Let $x$ be $\mathrm{0.2555...}$
$=>10x=\mathrm{2.555.....}$
$=>100x=\mathrm{25.555..}$
$=>100x=23+2.555$

$=>100x=23+10x$

$=>100x-10x=23$
$=>90x=23$
$=>x=\frac{23}{90}$