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

Guest Jul 27, 2022

#1

#2**0 **

Your answer is wrong, the number is more than the denominator, so the fraction will be greater than 1...

BuilderBoi
Jul 28, 2022

#3**0 **

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 \(x = {72 \over 99}\)

BuilderBoi Jul 28, 2022