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: 69


The value of a digit varies according to the position it occupies in a numeral. Place values varies with the position of the digit with exponents of the base. Place values of a four-digit base six number are: \[{{6}^{3}},{{6}^{2}},{{6}^{1}},{{6}^{0}}\] For example: Place values of number \[{{1442}_{\operatorname{six}}}\]are, \[\begin{align} & {{1442}_{\operatorname{six}}}=\left( 1\times {{6}^{3}} \right)+\left( 4\times {{6}^{2}} \right)+\left( 4\times {{6}^{1}} \right)+\left( 2\times {{6}^{0}} \right) \\ & =216+144+24+2 \\ & =386 \end{align}\]
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