Problem:
The population of the United States in 1980 was 226,504,825. The area of the country is 3,615,122 square miles. There are (5280)2 square feet in one square mile. Which number below best approximates the average number of square feet per person?
Answer Choices:
A. 5000
B. 10000
C. 50000
D. 100000
E. 500000
Solution:
With about 230 million people and under 4 million square miles, there are about 60 people per square mile. Since a square mile is about (5000ft)2=25 million square feet, that gives approximately 25/60 of a million square feet per person. The closest answer is (E).
OR
Consider the approximation obtained by rounding to two significant digits, using scientific notation and simplifying. We obtain
2.3×108 people (3.6×106mi2)(5.3×103ft/mi)2​=2.3(3.6)(5.3)2​×106+6−8ft2/ person
Now, 3.6/2.3 is slightly more than 1.5, and (5.3)2 is between 25 and 30. Thus the exact answer is about (28×1.5)(10,000)=420,000. The closest answer to this among those given is (E).