Answer
$\frac{251}{990}$
Work Step by Step
We express the number as a sum of fractions:
$0.25353...=0.2+\frac{53}{1000}+\frac{53}{100,000}+\frac{53}{10,000,000}+...$
We know that this represents an infinite geometric series with $a=0.053$ and $r= \frac{1}{100}$ (added to $0.2$).
We know the sum of an infinite geometric series is:
$S_{\infty}=\frac{a}{1-r}$
$S_{\infty}=\frac{0.053}{1-\frac{1}{100}}=\frac{53}{990}$
Thus the original number is:
$0.2+\frac{53}{990}=\frac{2}{10}+\frac{53}{990}=\frac{2*99+53}{990}=\frac{251}{990}$
