Thinking Mathematically (6th Edition)

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

Chapter 5 - Number Representation and Calculation - Chapter Summary, Review, and Test - Review Exercises: 19

Answer

$89 = 324_{\text{five}}$

Work Step by Step

The place values for base five are $..., 5^3, 5^2, 5^1, 1$. The place values that are less than or equal to $89$ are $5^2, 5^1, 1$. Divide $89$ by $5^2$ or $25$: $89\div 25 = 3$ remainder $14$ Divide the remainder $14$ by $5^1$ or $5$: $14 \div 5 = 2$ remainder $4$ Divide the remainder $4$ by $1$: $4 \div 1 = 4$ Thus, $89 = (3 \times 5^2) + (2 \times 5^1) + (4 \times 1) \\89 = 324_{\text{five}}$
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