Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Section 1.7 - Scientific Notation - Exercise Set - Page 91: 88


The statement makes sense. $ (4 \times10^{3}) + (3 \times 10^{2})$=$4.3\times 10^{3}$

Work Step by Step

$$ (4 \times10^{3}) + (3 \times 10^{2}) = 43 \times 10^{2}$$ To add scientific notations with different exponents, the exponent of 10 is the smaller expression must be adjusted such that it matches that of the larger expression. In this case, the smaller exponent is $2$ while the larger exponent is $3$. Determine the number by which to increase the smaller exponent by so it is equal to the larger exponent. Thus, $$3-2 = 1$$ Increase the smaller exponent by this number and move the decimal point of the number with the smaller exponent to the left the same number of places. Thus, $$3 \times 10^{2} = 0.3\times 10^{3}$$ Rewrite the whole expression: $$4\times 10^{3} +0.3\times 10^{3}$$ $$=4.3\times 10^{3}$$ On the other hand, $43 \times 10^{2}$ can be further converted in scientific notation as: $$4.3 \times 10^{3}$$ such that the numerical factor is between 1 and 10. The statement, therefore, makes sense.
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