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: 119

Answer

The average dollar amount each beneficiary receives is $\frac{7.78}{5.6}$ $\times$ $10^{4}$, or approximately 1.38928571429 $\times$ $10^{4}$.

Work Step by Step

We need to write 778,000,000,000 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 7.78 The decimal point has moved 11 places, so the exponent of 10 will be 11. So, 778,000,000,000 = 7.78 $\times$ $10^{11}$ Also, we need to convert 56,000,000 to scientific notation. We follow the same procedure. The number greater than or equal to 1 and less than 10 will be 5.6 The decimal point has moved 7 places, so the exponent of 10 will be 7. So, 56,000,000 = 5.6 $\times$ $10^{7}$ To find the average dollar amount each beneficiary receives, we divide 7.78 $\times$ $10^{11}$ by 5.6 $\times$ $10^{7}$. So, $\frac{7.78 \times 10^{11}}{5.6 \times 10^{7}}$ = $\frac{7.78}{5.6}$ $\times$ $10^{11-7}$ = $\frac{7.78}{5.6}$ $\times$ $10^{4}$ The average dollar amount each beneficiary receives is $\frac{7.78}{5.6}$ $\times$ $10^{4}$, or approximately 1.38928571429 $\times$ $10^{4}$.
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