Answer
$\dfrac{1}{15}$
Work Step by Step
Here, $0.06666=\dfrac{6}{100}(1+ \dfrac{1}{10}+ \dfrac{1}{(10)^2}+..)$
Formula to find the sum of a geometric series$1+ \dfrac{1}{10}+ \dfrac{1}{(10)^2}+..$ is $S=\dfrac{a}{1-r}$
Since we have , $a=1, r=\dfrac{1}{10}=0.1$;
Then , we get $S=\dfrac{6}{100}(\dfrac{1}{1-0.1})=\dfrac{1}{15}$
