Use the Formula for the Sum of an Infinite Geometric Series
-$0 . \overline { 858 }$
A) $\frac { 286 } { 333 }$
B) $\frac { 8 } { 9 }$
C) $\frac { 429 } { 500 }$
D) $\frac { 37 } { 125 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.\overline{858}$ can be expressed as an infinite geometric series with the first term $a = 0.858$ and common ratio $r = \frac{1}{1000}$ (since the pattern repeats every three decimal places). Using the formula for the sum of an infinite geometric series, $S = \frac{a}{1 - r}$, we get $S = \frac{0.858}{1 - \frac{1}{1000}} = \frac{0.858}{\frac{999}{1000}} = \frac{0.858 \times 1000}{999} = \frac{858}{999} = \frac{286}{333}$.

Use the Formula for the Sum of an Infinite Geometric 0.858‾0 . \overline { 858 }0.858

Use the Formula for the Sum of an Infinite Geometric $0 . \overline { 858 }$