Answer
$\frac{5017}{495}$
Work Step by Step
$10.135135135$
$=10.1 + \frac{35}{10^{3}} + \frac{35}{10^{5}}+\frac{35}{10^{7}}+...$
$a=\frac{35}{10^{3}}$ and $r= \frac{1}{10^{2}}$
$10.135135135 =10.1+ \frac{\frac{35}{10^{3}}}{1-\frac{1}{10^{2}}}$
$=10.1 + \frac{\frac{35}{1000}}{\frac{99}{100}}$
$=\frac{101}{10} + \frac{35}{990}$
$= \frac{10034}{990}=\frac{5017}{495}$
