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: 10

Answer

$10102_{three}$

Work Step by Step

Rightmost column: $1+1=2\times 1=2_{three}$ record the $2$, no carry, $\left[\begin{array}{lllll} & & & & \\ & 1 & 0 & 2 & 1_{three}\\ + & 2 & 0 & 1 & 1_{three}\\ & - & - & - & -\\ & & & & 2_{three} \end{array}\right.$ Next column: $1+2=3=1\times 3+0\times 1=10_{three}$ record the $0$, carry the 1. $\left[\begin{array}{lllll} & & 1 & & \\ & 1 & 0 & 2 & 1_{three}\\ + & 2 & 0 & 1 & 1_{three}\\ & - & - & - & -\\ & & & 0 & 2_{three} \end{array}\right.$ Next column: $1+0+0=1=1\times 1=1_{three}$ record the $1$, no carry, $\left[\begin{array}{lllll} & & 1 & & \\ & 1 & 0 & 2 & 1_{three}\\ + & 2 & 0 & 1 & 1_{three}\\ & - & - & - & -\\ & & 1 & 0 & 2_{three} \end{array}\right.$ Next column: $1+2=3=1\times 3+0\times 1=10_{three}$ record the $10$ result: $10102_{three}$
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