Chapter 11 - Section 11.2 - Series - 11.2 Exercises - Page 716: 52

$=\dfrac {46}{99}$

$0.\overline {46}=0.464646\ldots =\dfrac {46}{100}+\dfrac {46}{100^{2}}+\dfrac {46}{100^{3}}=\dfrac {a_{1}}{1-r};a_{1}=\dfrac {46}{100};r=\dfrac {1}{100}\Rightarrow 0.\overline {46}=\dfrac {\dfrac {46}{100}}{1-\dfrac {1}{100}}=\dfrac {46}{99}$