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Write the repeating decimal $0.\overline{515}$ as a fully simplified fraction.

 Apr 2, 2021
 #1
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Let $x=0.\overline{515}$.

 

Multiplying both sides by 1000 gives: $1000x=515.\overline{515}$

 

Subtract x from 1000x to get rid of the repeating part: $1000x-x=515$ so $999x=515$

 

Dividing both sides by 999 gives $\boxed{x=0.\overline{515}=515/999}$

 Apr 2, 2021

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