Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction
-$0 . \overline{5}$
A) $\frac{5}{11}$

B) $\frac{5}{7}$

C) $\frac{5}{9}$

D) $\frac{5}{10}$

Question

Use an infinite geometric series to rewrite the repeating decimal as a lowest-terms fraction
-$0 . \overline{5}$
A) $\frac{5}{11}$

B) $\frac{5}{7}$

C) $\frac{5}{9}$

D) $\frac{5}{10}$

Quizplus · Accepted Answer

The repeating decimal $0.\overline{5}$ can be expressed as an infinite geometric series: $0.5 + 0.05 + 0.005 + \cdots$. The first term $a = 0.5$ and the common ratio $r = \frac{1}{10}$. Using the formula for the sum of an infinite geometric series, $S = \frac{a}{1 - r}$, we get $S = \frac{0.5}{1 - \frac{1}{10}} = \frac{0.5}{\frac{9}{10}} = \frac{5}{9}$.

Use an Infinite Geometric Series to Rewrite the Repeating Decimal 0.5‾0 . \overline{5}0.5

Use an Infinite Geometric Series to Rewrite the Repeating Decimal $0 . \overline{5}$