## General Chemistry: Principles and Modern Applications (10th Edition)

Published by Pearson Prentice Hal

# Chapter 1 - Matter: Its Properties and Measurement - Exercises - Units of Measurement - Page 27: 30

#### Answer

a) There are $10^{6}$ square meters in 1 square kilometer. b) There are $10^{6}$ cubic centimeters in 1 cubic meter. c) There are 2589988.11 square meters in 1 square mile

#### Work Step by Step

a) From $km^{2}$ to $m^{2}$ is 3 units smaller. So one has to multiply the number in $km^{2}$ with $10^{6}$ to convert it into $m^{2}$. (Note: do not multiply it with 1000, since it is a unit of area). So 1 $km^{2}$ is $10^{6}$ $m^{2}$. In other words, there are $10^{6}$ square meters in 1 square kilometer. b) From $m^{3}$ to $cm^{3}$ is 2 units smaller. So one has to multiply the number in $m^{3}$ with $10^{6}$ to convert it into $cm^{3}$. (Note: do not multiply it with 100, since it is a unit of volume). So 1 $m^{3}$ = $10^{6}$$cm^{3}$. In other words, there are $10^{6}$ cubic centimeters in 1 cubic meter. c) 1 mi = 5280 ft So 1 $mi^{2}$ = $5280^{2}$ $ft^{2}$ = 27878400 $ft^{2}$ 1 ft = 0.3048 m So 1 $ft^{2}$ = $0.3048^{2}$ $m^{2}$ = 0.09290304 $m^{2}$ So 1 $mi^{2}$ = 27878400 * 0.09290304 $m^{2}$ = 2589988.11 $m^{2}$. In other words, there are 2589988.11 square meters in 1 square mile.

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