Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 1 - Section 1.3 - The Real Numbers - Exercise Set - Page 42: 32

Answer

$1.1\overline{6}$

Work Step by Step

The denominator can be not expanded to 10,100,1000... because it has factors other than 2 and 5. Long division: $\begin{array}{lllllll} & & 1 & .1 & 6 & 6... & \\ & - & -- & -- & -- & -- & \\ 6 & ) & 7 & .0 & 0 & 0 & \\ & & 6 & & & & \\ & & -- & & & & \\ & & 1 & 0 & & & \\ & & & 6 & & & \\ & & -- & -- & & & \\ & & & 4 & 0 & & \\ & & & 3 & 6 & & \\ & & & -- & -- & & \\ & & & & 4 & 0 & repeats \end{array}$ $-\displaystyle \frac{7}{6}=-7\div 6=1.16666...=1.1\overline{6}$
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