Thinking Mathematically (6th Edition)

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

Chapter 4 - Number Representation and Calculation - 4.2 Number Bases in Positional Systems - Exercise Set 4.2 - Page 227: 70


Suppose a number\[abcd\]with 4 digits to the base \[e\] has place values. \[{{e}^{3}},{{e}^{2}},{{e}^{1}},{{e}^{0}}\] Multiply each digit in the numeral with place-value. Then, sum yields the numeral value in base ten. That is., \[abc{{d}_{e}}=\left( a\times {{e}^{3}} \right)+\left( b\times {{e}^{2}} \right)+\left( c\times e \right)+\left( d\times 1 \right)\] The number \[abcd\] is converted to base ten. For example; \[\begin{align} & {{4327}_{six}}=\left( 4\times {{6}^{3}} \right)+\left( 3\times {{6}^{2}} \right)+\left( 2\times {{6}^{1}} \right)+\left( 7\times 1 \right) \\ & =991 \end{align}\]
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