Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6: 120

Answer

The average number of pennies produced per person is 16.

Work Step by Step

We need to write 4,939,000,000 as the product of a number greater than or equal to 1 and less than 10, and an integral power of 10. The number greater than or equal to 1 and less than 10 will be 4.939 The decimal point has moved 9 places, so the exponent of 10 will be 9. So, 4,939,000,000 = 4.939 $\times$ $10^{9}$ Also, we need to convert 310,000,000 to scientific notation. We follow the same procedure. The number greater than or equal to 1 and less than 10 will be 3.1 The decimal point has moved 8 places, so the exponent of 10 will be 8. So, 310,000,000 = 3.1 $\times$ $10^{8}$ To find the average number of pennies produced per person, we divide 4.939 $\times$ $10^{9}$ by 3.1 $\times$ $10^{8}$. So, $\frac{4.939 \times 10^{9}}{3.1 \times 10^{8}}$ = $\frac{4.939}{3.1}$ $\times$ $10^{9-8}$ = 1.59322580645 $\times$ 10 = 15.9322580645, or approximately 16.
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