Answer
$\frac{4}{9}$
Work Step by Step
$
\sum_{i=1}^{\infty} \frac{4}{10^{i}} =\sum_{i=1}^{\infty} 4\left(\frac{1}{10}\right)^{i}
$
This is a geometric series with initial term $a=4\left(\frac{1}{10}\right)^{1}=\frac{4}{10}$
Note : Initial term is the term that corresponds to $i=1$ in this case
Common ratio is $r=\frac{1}{10}$
Sum of the series $=\frac{a}{1-r}=\frac{\frac{4}{10}}{1-\frac{1}{10}}=\frac{\frac{4}{10}}{\frac{9}{10}}=\frac{4}{9}$
