Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 736: 52

$0.46464646 = \frac{46}{99}$

$0.4646464646$ $=\frac{46}{10^{2}}+\frac{46}{10^{4}}+\frac{46}{10^{6}}+...$ $=\Sigma^{\infty}_{n=1}46(\frac{1}{10^{2}})^{n}$ $a=\frac{46}{100}$ and $r=\frac{1}{100}$ $0.46464646464646 = \frac{a}{1-r}$ $=\frac{\frac{46}{100}}{1-\frac{1}{100}}$ $=\frac{46}{99}$