Express the repeating decimal as a fraction in lowest terms.
-$$0 . \overline { 4 } = \frac { 4 } { 10 } + \frac { 4 } { 100 } + \frac { 4 } { 1,000 } + \frac { 4 } { 10,000 } \ldots$$
A) $\frac { 111 } { 250 }$
B) $\frac { 4 } { 99 }$
C) $\frac { 11 } { 25 }$
D) $\frac { 4 } { 9 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.\overline{4}$ can be expressed as $\frac{4}{9}$ because it represents an infinite geometric series with the first term $\frac{4}{10}$ and a common ratio of $\frac{1}{10}$. Solving the series gives $\frac{4}{9}$.

Express the Repeating Decimal as a Fraction in Lowest Terms 0.4‾=410+4100+41,000+410,000…0 . \overline { 4 } = \frac { 4 } { 10 } + \frac { 4 } { 100 } + \frac { 4 } { 1,000 } + \frac { 4 } { 10,000 } \ldots0.4=104​+1004​+1,0004​+10,0004​…

Express the Repeating Decimal as a Fraction in Lowest Terms $0 . \overline { 4 } = \frac { 4 } { 10 } + \frac { 4 } { 100 } + \frac { 4 } { 1,000 } + \frac { 4 } { 10,000 } \ldots$