Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 24: 99

Answer

$1.332 \times 10^{21}$ liters

Work Step by Step

We need to measure the volume of the oceans in liters. We are given the surface area of $3.6 \times 10^{14} $m$^2$ and depth of $3.7 \times 10^{3} $m. And we know that 1 cubic meter of ocean contains 1000 liters. First we need to calculate how many cubic meters there are all together. For that we simply multiply the surface area by the depth. $(3.6 \times 10^{14}) \times (3.7 \times 10^{3})$ To multiply these in scientific notation we multiply the first number of each together, then we add the exponents of 10. $3.6 \times 3.7 = 13.32$ $10^{14+3} = 10^{17}$ $13.32 \times 10^{17}$ For proper scientific notation however we need to move the decimal place to the left by one place and increase the exponent by one. $1.332 \times 10^{18}$ cubic meters Now we multiply by 1000 which we can simplify by putting into scientific notation. $1 \times 10^3$ $(1.332 \times 10^{18}) \times (1 \times 10^3)$ $1.332 \times 1 = 1.332$ $10^{18+3}= 10^{21}$ Giving us an answer of $1.332 \times 10^{21}$ liters
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