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: 45

Answer

$1442_{\text{six}}$

Work Step by Step

The place values of base six are: $...,6^4, 6^3, 6^2, 6^1, 1$. The place values that are less than or equal to $386$ are $6^3$, $6^2$, $6^1$, and $1$ Divide $386$ by $6^3$ or $216$ to obtain: $386 \div 216 = 1$ remainder $170$ Divide the remainder $1701$ by $6^2$ or $36$ to obtain: $170 \div 36 = 4$ remainder $26$ Divide the remainder $26$ by $6^1$ or $6$ to obtain: $26 \div 6 = 4$ remainder $2$ Divide the remainder $2$ by $1$ to obtain: $2\div 1 = 2$ remainder $0$ Thus, $386=(1 \times 6^3) + (4 \times 6^2) + (4 \times 6^1) + (2 \times 1) \\386=1442_{\text{six}}$
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