Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 287: 145


A rational number can be expressed as a decimal by dividing the denominator to the numerator. The resulting decimal will either terminate, which is known as terminating decimal, or it will have a digit or block of digits that repeats itself, which is known as repeating decimal.

Work Step by Step

An example of writing a rational number as decimal is shown below: The rational number \[\frac{6}{11}\] can be written in decimal form as follows: \[11\overset{0.54}{\overline{\left){\begin{align} & 6.000 \\ & \underline{5\,\,5} \\ & \,\,\,\,50 \\ & \underline{\,\,\,\,44} \\ & \,\,\,\,\,\,\,60 \\ \end{align}}\right.}}\] Hence, \[\frac{6}{11}=0.\overline{54}\]
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