Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 1 - Foundations for Algebra - Chapter Test: 18

Answer

a) Rational b) Irrational

Work Step by Step

a) A rational number is defined as a number that can be written as ab where a and b are integers when b is not zero. Any terminating decimal is a rational number since it can be rewriten as a fraction where the decimal part of the number is the numerator and the denominator is the power of 10 corresponding to the rightmost digit. a) 0.2324 is a rational number. b) Use a calculator to find $\sqrt {46}$ . The result is 6.7823299831... This is a non-terminating decimal. Since you cannot determine the place value of the rightmost digit, a non-terminating decimal cannot be written as ab where a and b are integers when b is not zero. This means $\sqrt {46}$ is not a rational number, so it is an irrational number.
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