Question

Convert 8.132132132 … to a rational expression in the form of a over b, where b ≠ 0.

Answer 1

Let $x=8.132132132\ldots$.

Then $1000x=8132.132132132\ldots$.

Then $1000x-x=999x=8124$. The non-integer parts cancel.

So you end up with

$x=\dfrac{8124}{999}=\dfrac{2708}{333}$