Answer
$\dfrac{7}{9}$
Work Step by Step
Here, $0.7777= \dfrac{7}{10}+\dfrac{7}{(10)^2}+\dfrac{7}{(10)^3}+....=\dfrac{7}{10}(1+ \dfrac{1}{10}+ \dfrac{1}{(10)^2}+..)$
Formula to find the sum of a geometric series $1+ \dfrac{1}{10}+ \dfrac{1}{(10)^2}+..$ is $S=\dfrac{a}{1-r}$
Now, $a=1, r=\dfrac{1}{10}=0.01$;
Then,we have $S=\dfrac{7}{10}(\dfrac{1}{1-0.01})=\dfrac{7}{9}$
