Answer
$\frac{5}{66}$
Work Step by Step
$0.0\overline {75}=0.0757575\ldots =\dfrac {1}{10}\left( 0.7575\ldots \right) =\dfrac {1}{10}\left( \dfrac {75}{100}+\dfrac {75}{1002}+\dfrac {75}{1003}\right) =\dfrac {1}{10}\dfrac {a_{1}}{1-r}=\dfrac {1}{10}\dfrac {\dfrac {75}{100}}{1-\dfrac {1}{100}}=\dfrac {75}{990}=\dfrac {5}{66}$
