Respuesta :

Let [tex]x=8.132132132\ldots[/tex].

Then [tex]1000x=8132.132132132\ldots[/tex].

Then [tex]1000x-x=999x=8124[/tex]. The non-integer parts cancel.

So you end up with

[tex]x=\dfrac{8124}{999}=\dfrac{2708}{333}[/tex]