Question

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

$\mathrm{0.404040...}$ =$\frac{40}{q}$, then what is the value of $q$ ?

Answer 1

Let $x=\mathrm{0.404040...}$
$=>100x=\mathrm{40.4040...}$
$=>100x=40+\mathrm{0.4040...}$
$=>100x=40+x$
$=>100x-x=40$
$=>99x=40$
$=>x=\frac{40}{99}$

Hence, $q=99$