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: 122

Answer

The diameter of Earth is approximately 8091 miles.

Work Step by Step

Let x represent the diameter of Earth. The diameter of Jupiter, which is approximately 89,000 miles, is 11 times larger than the diameter of Earth, so it is 11 $\times$ x = 11x. We need to write 89,000 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 8.9. The decimal point has moved 4 places, so the exponent of 10 will be 4. So, 89,000 = 8.9 $\times$ $10^{4}$ Since the diameter of Jupiter is also 11x, we solve the following equation: 11x = 8.9 $\times$ $10^{4}$ Divide both sides by 11. x = $\frac{8.9}{11}$ $\times$ $10^{4}$ = 0.809090 $\times$ $10^{4}$ = 8090.9 $\approx$ 8091 miles The diameter of Earth is approximately 8091 miles.
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