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

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01-06-2018
Mathematics

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

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LammettHash LammettHash · Answer 1 · 2018-06-01T17:43:37+02:00

LammettHash LammettHash

01-06-2018

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]

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