Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.2 Negative Exponents and Scientific Notations - 4.2 Exercise Set - Page 245: 137

Answer

$600,000$ trees in New York City can clean $3\cdot 10^{8}mi$ of car traffic in a year.

Work Step by Step

$1$ tree$->500mi$ $600,000$ trees$->500\cdot 600,000mi$. $ 500\cdot 600,000\qquad$... write as powers of $10$. $=5\cdot 10^{2}\cdot 6\cdot 10^{5}\qquad$...apply The Product Rule $a^{m}\cdot a^{n}=a^{m+n}$ to solve $10^{2}\cdot 10^{5}$. $=5\cdot 6\cdot 10^{2+5}\qquad$... simplify. $=30\cdot 10^{7}\qquad$...write in scientific notation $N\cdot 10^{m},\ 1\leq N<10,\ N$ expressed in decimal notation, and $m$ as an integer. $=3\cdot 10\cdot 10^{7}\qquad$...apply The Product Rule again. $=3\cdot 10^{1+7}$ $=3\cdot 10^{8}$
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