Answer
$$\frac{5}{11}$$
Work Step by Step
Let
$$
x=0 . \overline{45}=0.45454545 \ldots
$$
Then
\begin{aligned} 100 x-x &=45.45454545\cdots \cdots-0.45454545\cdots \\
99 x &=45 \\ x &=\frac{45}{99}=\frac{5}{11} \end{aligned}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 548: 38
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