Express the repeating decimal as a fraction in lowest terms.
-$$0 . \overline { 2 } = \frac { 2 } { 10 } + \frac { 2 } { 100 } + \frac { 2 } { 1,000 } + \frac { 2 } { 10,000 } \ldots$$
A) $\frac { 2 } { 9 }$
B) $\frac { 2 } { 99 }$
C) $\frac { 11 } { 50 }$
D) $\frac { 111 } { 500 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.\overline{2}$ represents an infinite geometric series with the first term $a = \frac{2}{10}$ and common ratio $r = \frac{1}{10}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, substituting the values gives $S = \frac{\frac{2}{10}}{1 - \frac{1}{10}} = \frac{2}{9}$, which simplifies to $\frac{2}{9}$.

Express the Repeating Decimal as a Fraction in Lowest Terms 0.2‾=210+2100+21,000+210,000…0 . \overline { 2 } = \frac { 2 } { 10 } + \frac { 2 } { 100 } + \frac { 2 } { 1,000 } + \frac { 2 } { 10,000 } \ldots0.2=102​+1002​+1,0002​+10,0002​…

Express the Repeating Decimal as a Fraction in Lowest Terms $0 . \overline { 2 } = \frac { 2 } { 10 } + \frac { 2 } { 100 } + \frac { 2 } { 1,000 } + \frac { 2 } { 10,000 } \ldots$