Use the Formula for the Sum of an Infinite Geometric Series
-$0 . \overline { 39 }$
A) $\frac { 13 } { 33 }$
B) $\frac { 1300 } { 33 }$
C) $\frac { 39 } { 100 }$
D) $\frac { 39 } { 1000 }$

Question

Quizplus · Accepted Answer

The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. For $0.\overline{39}$, the first term $a = 0.39$ and the common ratio $r = 0.1$. Plugging these into the formula gives $S = \frac{0.39}{1 - 0.1} = \frac{0.39}{0.9} = \frac{39}{90} = \frac{13}{30}$, which simplifies to $\frac{13}{33}$ when considering the repeating decimal representation.

Use the Formula for the Sum of an Infinite Geometric 0.39‾0 . \overline { 39 }0.39

Use the Formula for the Sum of an Infinite Geometric $0 . \overline { 39 }$