Question

By which number should the recurring decimal $\mathrm{1.242424.....}$ be multiplied to convert it into $\frac{p}{q}$ form?

Answer 1

Let $x=\mathrm{1.24242424...}$

$100x=\mathrm{124.242424...}$

$\Rightarrow 100x-x=\mathrm{124.242424...}-\mathrm{1.24242424...}$

$\Rightarrow 99x=123$

$\Rightarrow x=\frac{123}{99}=\frac{41}{33}$

$\therefore x=\frac{41}{33}$ is in $\frac{p}{q}$ form.