Question

What is 0.03 (with the 3 repeating)/0.03 (with both the 0 and the 3 repeating) Express your answer as a mixed number.

Answer 1

$0.0\overline{3}=\dfrac{1}{30}\\0.\overline{03}=\dfrac{1}{33}\\\\\dfrac{0.0\overline{3}}{0.\overline{03}}=\dfrac{\dfrac{1}{30}}{\dfrac{1}{33}}=\dfrac{1}{30}\cdot33=\dfrac{11}{10}=1\dfrac{1}{10}$