Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 1 - Section 1.4 - Properties of Real Numbers and Algebraic Expressions - Exercise Set - Page 39: 31

Answer

0, no reciprocal

Work Step by Step

We are given that a number $a=0$. We know that the opposite of a number $a$ is $-a$, so the opposite of $a=0$ will be $-a=0$. In other words, the opposite of 0 is 0. We know that the reciprocal of a nonzero number $a$ is the number $\frac{1}{a}$, where $a\times\frac{1}{a}=1$ However, 0 has no reciprocal, because there is no number that, when multiplied by 0, results in a product of 1.
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