Provide an appropriate response.
-Convert the decimal $.100100100 \ldots$ to a fraction by writing it as the infinite series $\frac { 100 } { 1000 } + \frac { 100 } { 1000 ^ { 2 } } + \frac { 100 } { 1000 ^ { 3 } } + \ldots$
A) $0.099$

B) $\frac { 100 } { 999 }$

C) $0.1011011$

D) $0.101$

Question

Provide an appropriate response.
-Convert the decimal $.100100100 \ldots$ to a fraction by writing it as the infinite series $\frac { 100 } { 1000 } + \frac { 100 } { 1000 ^ { 2 } } + \frac { 100 } { 1000 ^ { 3 } } + \ldots$
A) $0.099$

B) $\frac { 100 } { 999 }$

C) $0.1011011$

D) $0.101$

Quizplus · Accepted Answer

This decimal is a repeating decimal, which can be represented as a geometric series with the first term $a = \frac{100}{1000}$ and the common ratio $r = \frac{1}{1000}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, which in this case is $S = \frac{\frac{100}{1000}}{1 - \frac{1}{1000}} = \frac{100}{999}$.

Provide an Appropriate Response .100100100….100100100 \ldots.100100100… To a Fraction by Writing It as the Infinite Series

Provide an Appropriate Response $.100100100 \ldots$ To a Fraction by Writing It as the Infinite Series