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What is $\frac{0.\overline{72}}{0.\overline{27}}$? Express your answer as a common fraction in lowest terms.

 Jul 27, 2022
 #1
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The expression reduces to 2/9.

 Jul 27, 2022
 #2
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Your answer is wrong, the number is more than the denominator, so the fraction will be greater than 1...

BuilderBoi  Jul 28, 2022
 #3
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I'll do the numerator, and you can do the denominator. 

 

For the numerator, let \(x = 0.{ \overline{72}}\). This means \(100x = {72. \overline{72}}\) (move the decimal point 2 places to the right)

 

Subtracting the 2 yields us \(99x = 72\) (the repeating parts cancel out)

 

Dividing by 99, we find that \(x = {72 \over 99}\)

 Jul 28, 2022

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