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: 18

Answer

$218_{nine}$

Work Step by Step

Start with rightmost column. $2$ is less than $3$. Borrow 1 $nine$ from the $1$ in the next column. In base ten: $(2+9)-3=8$ Record: $8_{nine}$ $\begin{array}{llll} & 7 & 1 & 2_{nine}\\ - & 4 & 8 & 3_{nine}\\ -- & -- & -- & --\\ & & & 8_{nine} \end{array}$ Next column: $(1-1)=0$ (we borrowed one eight) 0 is less than 8... borrow 1 nine from the 7 $(0+9)-8=1$ Record the $1$. $\begin{array}{llll} & 7 & 1 & 2_{nine}\\ - & 4 & 8 & 3_{nine}\\ -- & -- & -- & --\\ & & 1 & 8_{nine} \end{array}$ Next column: $7-1=6$ (one was borrowed) $6-4=2$ Record the 2. Result: $218_{nine}$
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