Solve each problem. See Example 12.
157.The U.S. budget first passed $1,000,000,000in 1917. Sev-
enty years later, in 1987, it exceeded $1,000,000,000,000
for the first time. The budget request for fiscal-year 2009
was $3,100,000,000,000.If stacked in dollar bills, this
amount would stretch 210,385mi, almost 90% of the dis-
tance to the moon. Write the four boldfaced numbers in
scientific notation. (Source:www.gpoaccess.gov, The New
York Times.)
158.By area, the largest of the fifty United States is Alaska, with land area of about
365,482,000acres, while the smallest is Rhode Island, with land area of about 677,000
acres. The total land area of the United States is about 2,271,343,000acres.Write these
three numbers in scientific notation. (Source:General Services Administration.)
159.In January 2010, the population of the United States was approximately 308.4 million.
(Source:U.S. Census Bureau.)
(a)Write the January 2010 population using scientific notation.
(b)Write $1 trillion, that is, $1,000,000,000,000, using scientific notation.
(c)Using your answers from parts (a) and (b), calculate how much each person in the
United States in the year 2010 would have had to contribute in order to make some-
one a trillionaire. Write this amount in standard notation to the nearest dollar.
160.In February 2010, the U.S. House of Representatives voted to allow the government to
go $1.9 trillion deeper in debt. Calculate how much additional debt this is for every U.S.
resident. Use the 2010 population of 308.4 million from Exercise 159,and write the
amount in standard notation to the nearest dollar. (Source: The Gazette.)
161.In 2009, the national debt of the U.S. government was about $11.5 trillion. Using
307.0 million as the population for that year, about how much was this per American?
Write the amount in standard notation to the nearest dollar. (Source: The Gazette.)
162.In the early years of the Powerball Lottery, a
player would choose five numbers from 1 through
49 and one number from 1 through 42. It can be
shown that there are about differ-
ent ways to do this. Suppose that a group of 2000 persons decided to purchase tickets
for all these numbers and each ticket cost $1.00. How much should each person have
expected to pay? (Source:www.powerball.com)
163.The speed of light is approximately cm per sec. How long will it take light to
travel cm?
164.The average distance from Earth to the sun is mi. How long would it take a
rocket, traveling at mph, to reach the sun?
165.A light-yearis the distance that light travels in one year. Find the number of miles in a
light-year if light travels mi per sec.
166.Use the information given in the previous two exercises to find the number of minutes
necessary for light from the sun to reach Earth.
167.In 2009, the estimated population of Luxembourg was
The population density was 493 people per square
mile. What is the area of Luxembourg, to the nearest square
mile? (Source: The World Factbook.)
168.In 2009, the population of Costa Rica was approximately
The population density was 83.3 people per
square kilometer. (Source: The World Factbook.)
(a)Write the population density in scientific notation.
(b)To the nearest square kilometer, what is the area of Costa Rica?
4.25* 106.
4.92* 105.
1.86* 105
2.9* 103
9.3* 107
9 * 1012
3 * 1010
8.009* 107
SECTION 5.1 Integer Exponents and Scientific Notation 277
FranceBelgium
GermanyLuxembourg