Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - Chapter R Test Prep - Review Exercises - Page 82: 24


$\color{blue}{-12, -6, -0.9, -\sqrt{4}, 0, \frac{1}{8}, \text{ and } 6}$

Work Step by Step

The set of integers is: $\left\{...-3, -2, -1, 0, 1, 2, 3, ...\right\}$ The set of rational numbers contain all the numbers that can be expressed as $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q \ne 0$. Note that: $-12=\dfrac{-24}{2}$ $-6 = \dfrac{12}{-2}$ $-0.9 = -\dfrac{9}{10}$ $-\sqrt{4} = -2 = -\dfrac{6}{3}$ $0=\dfrac{0}{1}$ $\dfrac{1}{8}=\dfrac{1}{8}$ $6=\dfrac{18}{3}$ The numbers above are quotients of two integers with non-zero denominators so they are all rational numbers. Thus, the rational among the elements of $K$ are: $\color{blue}{-12, -6, -0.9, -\sqrt{4}, 0, \frac{1}{8}, \text{ and } 6}$
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