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

User John Nagle
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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=(8124)/(999)=(2708)/(333)
User Brian Grinstead
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