Thinking Mathematically (6th Edition)

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

Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3: 17

Answer

$206_{eight}$

Work Step by Step

Start with the right-most column. $5$ is less than $7$. Borrow 1 $eight$ from the $7$ in the next column. In base ten: $(8+5)-7=6$ Record: $6_{eight}$ $\begin{array}{llll} & 4 & 7 & 5_{eight}\\ - & 2 & 6 & 7_{eight}\\ -- & -- & -- & --\\ & & & 6_{eight} \end{array}$ Next column: $(7-1)=6$ (we borrowed one eight) $6-6=0$ (no borrowing) Record the $0$. $\begin{array}{llll} & 4 & 7 & 5_{eight}\\ - & 2 & 6 & 7_{eight}\\ -- & -- & -- & --\\ & & 0 & 6_{eight} \end{array}$ Next column: $4-2=2$ Record the 2: Result: $206_{eight}$
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