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

 Dec 27, 2021
 #1
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The decimal fraction is:  0.515 515 515 515 ...

 

Let             x    =    0 . 515 515 515 515  ...

Then  1000x  =  515 . 515 515 515 515 ...

 

Subtracting the first line from the second:

              999x  =  515

                    x  =  515 / 999

 Dec 27, 2021

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