Answer
$=2+\dfrac {516}{999}=\dfrac {2514}{999}$
Work Step by Step
$2.\overline {516}=2.516516\ldots =2+\dfrac {516}{1000}+\dfrac {516}{10000}+\ldots =2+\dfrac {a_{1}}{1-r};a_{1}=\dfrac {516}{1000};r=\dfrac {1}{1000}\Rightarrow 2.\overline {516}=2+\dfrac {\dfrac {516}{1000}}{1-\dfrac {1}{1000}}=2+\dfrac {516}{999}=\dfrac {2514}{999}$
