Provide an appropriate response.
-Convert the decimal $980980980 \ldots$ to a fraction by writing it as the infinite series $\frac { 980 } { 1000 } + \frac { 980 } { 1000 ^ { 2 } } + \frac { 980 } { 1000 ^ { 3 } } + \ldots$
A) $\frac { 980 } { 999 }$
B) $0.979$
C) $0.98198198$
D) $0.981$

Question

Quizplus · Accepted Answer

This is a geometric series with the first term $a = \frac{980}{1000}$ and common ratio $r = \frac{1}{1000}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$. Substituting $a = \frac{980}{1000}$ and $r = \frac{1}{1000}$ gives $S = \frac{\frac{980}{1000}}{1 - \frac{1}{1000}} = \frac{980}{999}$.

Provide an Appropriate Response 980980980…980980980 \ldots980980980… To a Fraction by Writing It as the Infinite Series

Provide an Appropriate Response $980980980 \ldots$ To a Fraction by Writing It as the Infinite Series