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: 19

Answer

$366_{seven}$

Work Step by Step

Start with rightmost column. $3$ is less than $3$. Borrow 1 $seven$ from the $1$ in the next column. In base ten: $(7+3)-4=6$ Record: $6_{seven}$ $\begin{array}{llll} & 5 & 6 & 3_{seven}\\ - & 1 & 6 & 4_{seven}\\ -- & -- & -- & --\\ & & & 6_{seven} \end{array}$ Next column: $(6-1)=5$ (we borrowed one eight) $5$ is less than $6$... borrow 1 $seven$ from the $5$ $(5+7)-6=6$ Record the $6$. $\begin{array}{llll} & 5 & 6 & 3_{seven}\\ - & 1 & 6 & 4_{seven}\\ -- & -- & -- & --\\ & & 6 & 6_{seven} \end{array}$ Next column: $5-1=4$ (one was borrowed) $4-1=3$ Record the $3$. Result: $366_{seven}$
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