Express the repeating decimal as a fraction in lowest terms.
-$0 . \overline { 88 } = \frac { 88 } { 100 } + \frac { 88 } { 10,000 } + \frac { 88 } { 1,000,000 } + \ldots$
A) $\frac { 8 } { 9 }$
B) $\frac { 8888 } { 999 }$
C) $\frac { 8800 } { 999 }$
D) $\frac { 1111 } { 1250 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.\overline{88}$ can be expressed as a fraction by recognizing it as a geometric series with the first term $a = \frac{88}{100}$ and the common ratio $r = \frac{1}{100}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, which in this case is $S = \frac{\frac{88}{100}}{1 - \frac{1}{100}} = \frac{88}{100} \times \frac{100}{99} = \frac{88}{99}$. Simplifying $\frac{88}{99}$ gives $\frac{8}{9}$, making option A correct.

Express the Repeating Decimal as a Fraction in Lowest Terms 0.88‾=88100+8810,000+881,000,000+…0 . \overline { 88 } = \frac { 88 } { 100 } + \frac { 88 } { 10,000 } + \frac { 88 } { 1,000,000 } + \ldots0.88=10088​+10,00088​+1,000,00088​+…

Express the Repeating Decimal as a Fraction in Lowest Terms $0 . \overline { 88 } = \frac { 88 } { 100 } + \frac { 88 } { 10,000 } + \frac { 88 } { 1,000,000 } + \ldots$