Question

Write the rational number $13.\overline{514}$ in $\frac{p}{q}$ form.

Answer 1

Let $x=13.514514$…

$\Rightarrow 1000x=13514.514$

$1000x-x=|350|$

$\Rightarrow 999x=|350|$

$\Rightarrow x=\frac{|350|}{999}$.