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: 22

Answer

$7093 = 26452_{\text{seven}}$

Work Step by Step

The place values for base seven are $...,7^5, 7^4, 7^3, 7^2, 7^1, 1$. The place values that are less than or equal to $7093$ are $7^4, 7^3, 7^2, 7^1, 1$. Divide $7093$ by $7^4$ or $2401$: $7093 \div 2041 = 2$ remainder $2291$ Divide the remainder $2291$ by $7^3$ or $343$: $2291 \div 343 =6$ remainder $233$ Divide the remainder $233$ by $7^2$ or $49$: $233 \div 49 = 4$ remainder $37$ Divide the remainder $37$ by $7^1$ or $7$: $37 \div 7 = 5$ remainder $2$ Divide the remainder $2$ by $1$: $2 \div 1 = 2$ Thus, $7093 = (2 \times 7^4) + (6 \times 7^3) + (4 \times 7^2) +(5 \times 7^1)+ (2 \times 1) \\7093 = 26452_{\text{seven}}$
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