Answer
$\dfrac{1}{15}$
Work Step by Step
We have:
$0.06666=\dfrac{6}{100}(1+ \dfrac{1}{10}+ \dfrac{1}{(10)^2}+..)$
The sum of a geometric series $1+ \dfrac{1}{10}+ \dfrac{1}{(10)^2}+..$ can be found as:
$S=\dfrac{a}{1-r}$
Here, $a=1, r=\dfrac{1}{10}=0.1$;
Thus,
$S=\dfrac{6}{100}(\dfrac{1}{1-0.1})=\dfrac{1}{15}$