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: 31

Answer

$ 3114_{eight}$

Work Step by Step

$(4\times 3)_{10}=(12)_{10}=1\times 8+4=(14)_{8}$ Record the $4$; carry the $1$. $\begin{array}{llll} & 6 & 2 & 3_{eight}\\ \times & & & 4_{eight}\\ -- & -- & -- & --\\ & & & 4_{eight} \end{array}$ $(4\times 2+1)_{10}=(9)_{10}=1\times 8+1=(11)_{8}$ Record the $1$; carry the $1$. $\begin{array}{llll} & 6 & 2 & 3_{eight}\\ \times & & & 4_{eight}\\ -- & -- & -- & --\\ & & 1 & 4_{eight} \end{array}$ $(4\times 6+1)_{10}=(25)_{10}=3\times 8+1=(31)_{8}$ Record the $31:$ Result:$ 3114_{eight}$
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