What is $\frac{0.\overline{72}}{0.\overline{27}}$? Express your answer as a common fraction in lowest terms.
Your answer is wrong, the number is more than the denominator, so the fraction will be greater than 1...
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 \(x = {72 \over 99}\)