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

$\frac{4\mathrm{.}52}{b}ar(63)=4\mathrm{.}52636363$dots

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

A$.\frac{4\mathrm{.}52}{b}ar(63)={\displaystyle \underset{k=0}{\overset{}{}}}4\mathrm{.}52(0\mathrm{.}1{)}^k$

B$.\frac{4\mathrm{.}52}{b}ar(63)=4\mathrm{.}52{\displaystyle \underset{k=0}{\overset{}{}}}0\mathrm{.}0063(0\mathrm{.}01{)}^k$

C$.\frac{4\mathrm{.}52}{b}ar(63)=0\mathrm{.}0063{\displaystyle \underset{k=0}{\overset{}{}}}4\mathrm{.}52(0\mathrm{.}001{)}^k$

D$.\frac{4\mathrm{.}52}{b}ar(63)={\displaystyle \underset{k=0}{\overset{}{}}}0\mathrm{.}0063(0\mathrm{.}01{)}^k$

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

$\frac{4\mathrm{.}52}{b}ar(63)=($Type an integer or a simplified fraction.$)$