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APPLICATIONS
SOLVING REAL-LIFE PROBLEMS
Multiplying with Scientific Notation
EXAMPLE 5
AMAZON RIVER How much water does the Amazon River discharge into the
Am a z o n R i v e r
Pe
Atlantic Ocean each year?
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Brazil
Bo
liv
SOLUTION
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Pa
ra
gu
First find the number of seconds in a year. Then multiply the amount of water
discharged per second by the number of seconds per year to find the total amount
of water discharged into the Atlantic Ocean.
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Argentina
FE
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AL I
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GOAL 2
Use unit analysis to find the number of seconds in a year.
AMAZON RIVER
The Amazon River
in Brazil contributes more
water to Earth’s oceans than
any other river. Each second,
it discharges 4.2 ª 106 cubic
feet of water into the Atlantic
Ocean.
days hours minutes seconds
seconds
• • • = year day
hour
minute
year
365
24
• 1
1
•
60
1
•
60
1
= 31,536,000 ≈ 3.2 ª 107
There are about 3.2 ª 107 seconds in a year.
Multiply to find the total amount of water discharged by the Amazon River into
the Atlantic Ocean in one year.
4.2 ª 106 cubic feet
1 second
3.2 ª 107 seconds
1 year
Total amount of water = • = (4.2 ª 106) • (3.2 ª 107)
= 13.44 ª 1013
= 1.344 ª 1014
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History
STUDENT HELP
Look Back
For help with unit rates,
see p. 180.
One trillion is 1 ª 1012, so the total amount of water discharged into the
Atlantic Ocean by the Amazon River is about 134 trillion cubic feet per year.
EXAMPLE 6
Dividing with Scientific Notation
In 1867, the United States purchased Alaska from Russia for $7.2 million. The
total area of Alaska is about 3.78 ª 108 acres. What was the price per acre?
SOLUTION The price per acre is a unit rate.
Total price
Price per acre = Number of acres
7.2 ª 106
= 8
3.78 ª 10
7.2
3.78
= ª 10º2
≈ 0.019
䉴
472
The price was about 2¢ per acre.
Chapter 8 Exponents and Exponential Functions
7.2 million = 7.2 ª 106