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

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) $\frac { 4 } { 9 }$

Quizplus · Accepted Answer

The repeating decimal $0.\overline{4}$ can be expressed as $\frac{4}{9}$ because the repeating part is a single digit, and the fraction for a single repeating digit $n$ is $\frac{n}{9}$.

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 $0 . \overline { 4 } = \frac { 4 } { 10 } + \frac { 4 } { 100 } + \frac { 4 } { 1,000 } + \frac { 4 } { 10,000 } \ldots$