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: 29

Answer

$4011_{seven}$

Work Step by Step

$(5\times 3)_{10}=(15)_{10}=2\times 7+1=(21)_{7}$ Record the $1$; carry the $2$. $\begin{array}{llll} & 5 & 4 & 3_{seven}\\ \times & & & 5_{seven}\\ -- & -- & -- & --\\ & & & 1_{seven} \end{array}$ $(5\times 4+2)_{10}=(22)_{10}=3\times 7+1=(31)_{7}$ Record the $1$; carry the $3$. $\begin{array}{llll} & 5 & 4 & 3_{seven}\\ \times & & & 5_{seven}\\ -- & -- & -- & --\\ & & 1 & 1_{seven} \end{array}$ $(5\times 5+3)_{10}=(28)_{10}=4\times 7+0=(40)_{7}$ Record the $40.$ Result: $4011_{seven}$
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