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: 5

Answer

$1310_{five}$

Work Step by Step

Rightmost column: $2+3=5=1\times5+0\times1=10_{five}$ record the 0, carry the 1 $. \quad 1$ $.\ $3 4 $2_{five}$ $+ $4 1 $3_{five}$ $\_\_ \_ \_ \_$ $\qquad 0_{five}$ Next column: $1+4+1=6=1\times5+1\times1=11_{five}$ record the 1, carry the 1 $. \ 1\ 1$ $.\ $3 4 $2_{five}$ $+ $4 1 $3_{five}$ $\_\_ \_ \_ \_$ $\quad \ \ 1\ 0_{five}$ Next column: $1+3+4=8=1\times5+3\times1=11_{five}$ record the 13 $. \ 1\ 1$ $.\ $3 4 $2_{five}$ $+ $4 1 $3_{five}$ $\_\_ \_ \_ \_$ $\ 1\ 3\ 1\ 0_{five}$ Test in base 10 $3\times 5^{2}+4\times 5+2=97_{ten}$ $4\times 5^{2}+1\times 5+3=108_{ten}$ $1\times 125+3\times 25+1\times 5+0=205_{ten}$ $97+108=105$
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