Solve the problem.
-Write $0.77 \overline { 7 }$ as an infinite geometric series and use the formula for $\mathrm { S } _ { \infty }$ to write it as a rational number.
A) $\frac { 7 } { 100 }$
B) $\frac { 7 } { 10 }$
C) $\frac { 70 } { 9 }$
D) $\frac { 7 } { 9 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.77 \overline{7}$ can be expressed as the infinite geometric series $0.777...$ = $0.7 + 0.07 + 0.007 + \ldots$. The first term $a = 0.7$ and the common ratio $r = 0.1$. The sum of an infinite geometric series is given by $S_{\infty} = \frac{a}{1-r}$. Substituting the values, we get $S_{\infty} = \frac{0.7}{1-0.1} = \frac{0.7}{0.9} = \frac{7}{9}$.

Solve the Problem 0.777‾0.77 \overline { 7 }0.777 As an Infinite Geometric Series and Use the Formula For an Infinite

Solve the Problem $0.77 \overline { 7 }$ As an Infinite Geometric Series and Use the Formula For an Infinite