Question

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

$0.1\overline{34}$ is $\frac{m}{990}$, then $m$ is equal to

Answer 1

Let $x$ be $\mathrm{0.1343434...}$
$=>10x=\mathrm{1.3434...}\left(i\right)$
$=>10x\times 100=\mathrm{134.3434..}$
$=>1000x=133+1.3434$
$=>1000x=133+10x\left(fromi\right)$
$=>1000x-10x=133$
$=>x=\frac{133}{990}$