Provide an appropriate response.
-Convert the decimal $.676767 \ldots$ to a fraction by writing it as the infinite series $\frac { 67 } { 100 } + \frac { 67 } { 100 ^ { 2 } } + \frac { 67 } { 100 ^ { 3 } } + \ldots$
A) $\frac { 67 } { 99 }$
B) $0.66$
C) $0.68$
D) $0.68686869$

Question

Quizplus · Accepted Answer

This is a geometric series with the first term $a = \frac{67}{100}$ and common ratio $r = \frac{1}{100}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = \frac{67}{100}$ and $r = \frac{1}{100}$ gives $S = \frac{\frac{67}{100}}{1 - \frac{1}{100}} = \frac{67}{99}$.

Provide an Appropriate Response .676767….676767 \ldots.676767… To a Fraction by Writing It as the Infinite Series

Provide an Appropriate Response $.676767 \ldots$ To a Fraction by Writing It as the Infinite Series