The repeating decimal $0 . \overline { 2 }$ is expressed as a geometric series $0.2 + 0.02 + 0.002 + 0.0002 + \ldots$ . Write the decimal $0 . \overline { 2 }$ as the ratio of two integers.
A) $\frac { 2 } { 99 }$
B) $\frac { 7 } { 33 }$
C) $\frac { 2 } { 9 }$
D) $\frac { 5 } { 11 }$
E) $\frac { 9 } { 2 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.\overline{2}$ can be expressed as the infinite geometric series $0.2 + 0.02 + 0.002 + \ldots$ with the first term $a = 0.2$ and common ratio $r = 0.1$. The sum of this series is $\frac{a}{1-r} = \frac{0.2}{0.9} = \frac{2}{9}$.

The Repeating Decimal 0.2‾0 . \overline { 2 }0.2 Is Expressed as a Geometric Series

The Repeating Decimal $0 . \overline { 2 }$ Is Expressed as a Geometric Series