College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.3 - Page 740: 48


The repeating decimal as a fraction in lowest term = $\frac{83}{99}$

Work Step by Step

Given repeating decimal can be written as an infinite geometric series. = $\frac{83}{100}$ + $\frac{83}{10000}$ + $\frac{83}{1000000}$ + ..................................... First term $a_{1}$ = $\frac{83}{100}$ Common ratio = $\frac{1}{100}$ To express the repeating decimal as a fraction in lowest term we sum the obtained infinite geometric series. = $\frac{a_{1}}{1 - r}$ = $\frac{\frac{83}{100}}{1 - \frac{1}{100}}$ = $\frac{\frac{83}{100}}{\frac{99}{100}}$ = $\frac{83}{99}$
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