Write the repeating decimal first as a geometric series and then as a fraction $($a ratio of two integers$).$

$\frac{0.}{b}ar(2)=0\mathrm{.}2222$dots

Write the repeating decimal as a geometric series. Choose the correct answer below.

A$.\frac{0.}{b}ar(2)={\displaystyle \underset{k=0}{\overset{}{}}}0\mathrm{.}2(0\mathrm{.}1{)}^k$

B$.\frac{0.}{b}ar(2)={\displaystyle \underset{k=0}{\overset{}{}}}0\mathrm{.}2(0\mathrm{.}02{)}^k$

c$.\frac{0.}{b}ar(2)={\displaystyle \underset{k=0}{\overset{}{}}}0\mathrm{.}01(0\mathrm{.}21{)}^k$

D$.\frac{0.}{b}ar(2)={\displaystyle \underset{k=0}{\overset{}{}}}0\mathrm{.}2(0\mathrm{.}01{)}^k$

Write the repeating decimal as a fraction $($a ratio of two integers$)$

$\frac{0.}{b}ar(2)=($Type an integer or a simplified fraction.$)$