Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 4 - Number Representation and Calculation - Chapter 4 Test - Page 246: 12

Answer

The base ten numeral is\[53\].

Work Step by Step

To convert any numeral to base ten,multiply each digit of the given number with increasing powers of base value from the right side, according to places. \[\begin{align} & {{110101}_{t\text{wo}}}\,=\left( 1\times {{2}^{5}} \right)+\,\left( 1\times {{2}^{4}} \right)\,+\left( 0\times {{2}^{3}} \right)+\,\left( 1\times {{2}^{2}}\, \right)+\left( 0\times {{2}^{1}} \right)+\left( 1\times {{2}^{0}} \right) \\ & =\left( 1\times 32 \right)+\left( 1\times 16 \right)\,+\left( 1\times 4 \right)\,+\,\left( 1\times 1 \right) \\ & =32\,+16\,+4\,+1 \\ & =53 \end{align}\] The base ten numeral is\[53\].
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