Thinking Mathematically (6th Edition)

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

Chapter 4 - Number Representation and Calculation - 4.2 Number Bases in Positional Systems - Exercise Set 4.2: 57

Answer

$25_{\text{seven}}$

Work Step by Step

To convert a numeral in base five to a numeral in base seven, the following steps must be performed: (1) Convert the numeral in base five to base ten. $34_{\text{five}}=(3\times 5^1) + (4 \times 1)=15+4=19$ (2) Convert the result in Step (1) to a numeral in base 7 using division. Divide $19$ by $7$: $19 \div 7 = 2$ remainder $5$ Divide $5$ by $1$: $5 \div 1 = 5$ remainder Thus, $19 = (2 \times 7^1) + (5 \times 1) \\19= 25_{\text{seven}}$
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