#### Answer

$\frac{1}{3}$

#### Work Step by Step

The sum of an infinite geometric sequence can be obtained by the formula $S_n=\frac{a_1}{1-r}$ where $a_1$ is the first term and $r$ is the common ratio and $|r|\lt1$.
$0.\overline{3}=0.3+0.03+0.003+...$
Hence $S_n=\frac{0.3}{1-0.1}=\frac{1}{3}$