Answer
$\dfrac{2}{3}$
Work Step by Step
Write the decimal $0.\overline{6}$ as $0.6+0.06+0.006+...$
Thus, we have $S_{\infty}=\dfrac{a_1}{1-r}$
Here, $a_1=0.6,r=0.1$
Thus,
$0.\overline{6}=\dfrac{0.6}{1-0.1}=\dfrac{2}{3}$
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: 47
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