Answer
$\frac{71}{330}$
Work Step by Step
$0.2\overline {15}=\dfrac {1}{10}\left( 2+0.\overline {15}\right) =\dfrac {1}{5}+\dfrac {1}{10}\left( 0.\overline {15}\right) =\dfrac {1}{5}+\dfrac {1}{10}\left( \dfrac {15}{100}+\dfrac {15}{1002}+\dfrac {15}{1003}\right) =\dfrac {1}{5}+\dfrac {1}{10}\left( \dfrac {\dfrac {15}{100}}{1-\dfrac {1}{100}}\right) =\dfrac {1}{5}+\dfrac {1}{66}=\dfrac {71}{330}$
