Answer
$\dfrac{47}{99}$
Work Step by Step
Write the decimal $0.\overline{47}$ as $0.47+0.0047+0.000047+...$
Thus, we have $S_{\infty}=\dfrac{a_1}{1-r}$
Here, $a_1=0.47,r=0.01$
Thus,
$0.\overline{47}=\dfrac{0.47}{1-0.01}=\dfrac{47}{99}$
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 11 - Review Exercises - Page 870: 48
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