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: 48

Answer

$2502_{\text{eight}}$

Work Step by Step

The place values of base eight are: $...,8^4, 8^3, 8^2, 8^1, 1$. The place values that are less than or equal to $1346$ are $8^3, 8^2$, $8^1$, and $1$ Divide $1346$ by $8^3$ or $512$ to obtain: $1346 \div 512 = 2$ remainder $322$ Divide $322$ by $8^2$ or $64$ to obtain: $322 \div 64 = 5$ remainder $2$ Divide the remainder $2$ by $8^1$ or $8$ to obtain: $2 \div 8 = 0$ remainder $2$ Divide the remainder $2$ by $1$ to obtain: $2\div 1 = 2$ remainder $0$ Thus, $1346=(2 \times 8^3) + (5 \times 8^2) + (0 \times 8^1) + (2 \times 1) \\1346=2502_{\text{eight}}$
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