Answer
$\frac{1}{33}$
Work Step by Step
We express the number as a sum of fractions:
$0.030303 \ldots=\frac{3}{100}+\frac{3}{10,000}+\frac{3}{1,000,000}+\cdots$
We know that this represents an infinite geometric series with $a=0.03$ and $r= \frac{1}{100}$.
We know the sum of an infinite geometric series is:
$S_{\infty}=\frac{a}{1-r}$
$S_{\infty}=\frac{0.03}{1-\frac{1}{100}}=\frac{1}{33}$
