Answer
$=\dfrac {1}{9}$
Work Step by Step
$0.\overline {1}=0.1111...=\dfrac {1}{10}+\dfrac {1}{10^{2}}+\dfrac {1}{10^{3}}+\ldots =\dfrac {a_{1}}{1-r}=\dfrac {\dfrac {1}{10}}{1-\dfrac {1}{10}}=\dfrac {\dfrac {1}{10}}{\dfrac {9}{10}}=\dfrac {1}{9}$