Solve the problem.
-Use the formula $S _ { \infty }$ to write $0.49 \overline { 49 }$ as a fraction.
A) $\frac { 49 } { 99 }$
B) $\frac { 49 } { 1000 }$
C) $\frac { 4900 } { 99 }$
D) $\frac { 49 } { 100 }$

Question

Quizplus · Accepted Answer

The repeating decimal $0.49\overline{49}$ can be converted into a fraction using the formula for an infinite geometric series, $S_{\infty} = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = 0.49$ and $r = 0.01$ (since the pattern repeats every two decimal places, which is equivalent to dividing by 100). However, a more straightforward approach for repeating decimals is to set $x = 0.49\overline{49}$, multiply by a power of 10 to move the decimal point past the repeating part, subtract the original equation, and solve for $x$. This gives $x = \frac{49}{99}$, which is option A.

Solve the Problem S∞S _ { \infty }S∞​ To Write 0.4949‾0.49 \overline { 49 }0.4949

Solve the Problem $S _ { \infty }$ To Write $0.49 \overline { 49 }$