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 - Concept and Vocabulary Check: 5

Answer

Fill the blanks with ... 2 ... 1 ... 21 ... 1 ... 2 ... 2 ... 2 ... 0 ... 20 ... 201

Work Step by Step

We begin with $3\times 3=9=2\times 4+1\times 1=21_{four}$ Record the 1, carry the 2 $\begin{array}{lll} & 2 & \\ & 2 & 3_{four}\\ \times & & 3_{four}\\ -- & -- & --\\ & & 1_{four} \end{array}$ Next $3\times2 +2=8=2\times4+0\times1=20_{four}$ Record this: $\begin{array}{lll} & 2 & \\ & 2 & 3_{four}\\ \times & & 3_{four}\\ -- & -- & --\\ 2 & 0 & 1_{four} \end{array}$ (the result is $201_{four})$
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