Name: Date: Lesson 2.3 Multiplying and Dividing in Scientific Notation
Evaluate each expression in scientific notation, and round the coefficient to the nearest tenth.
1. 8.5 ? 1022 ? 9.52 ? 107 2.3.8 ? 103 4 4.86 ? 1022
3. 6.2 ? 105 ? 4.7 ? 1028 4.6.8 ? 1010 4 2.3 ? 1024
The table shows the approximate lengths, in miles, of some rivers in the
United States. Use the information to answer questions 5 to 7. Round your
answers to the nearest tenth.
Name of River
Length of River (mi)
Colorado River (Texas)
8.94 ? 102
Rio Grande
1.885 ? 103
Mississippi River
3.860 ? 103
© Marshall Cavendish International (Singapore) Private Limited.
5. About how many times as great as the length of Colorado River is the Mississippi
River?
6. About how many times as great as the length of Colorado River is the Rio
Grande?
7. About how many times as great as the length of the Rio Grande is the Mississippi
River?
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Name: Date: Solve. Show your work.
8. A certain type of bacteria can move at a speed of 220 micrometers per second.
a)What is the distance, in meters, moved by the bacteria after 12 hours?
Write your answer in scientific notation.
b)Another type of bacteria moves 8 ? 1027 meter per second. How far
does this bacteria move in 5.45 ? 109 seconds? Write your answer, in
micrometers, using scientific notation.
9. The diagram shows a cube with sides of length 8 meters. A smaller cube with
sides of length 3.5 meters has been cut out of the larger cube.
b)Find the volume of the solid after the small cube is removed. Write your
answer in scientific notation. Round the coefficient to the nearest tenth.
© Marshall Cavendish International (Singapore) Private Limited.
a)Find the volume, in cubic centimeters, of the large cube before the small
cube is cut out. Write your answer in scientific notation.
22 Chapter 2 Lesson 2.3
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Name: Date: Solve. Show your work.
10. The table shows some models of LCD televisions and their native pixel resolution.
Model
Native Pixel Resolution
A
1,280 ? 720
B
1,024 ? 768
C
1,366 ? 768
D
1,920 ? 1,080
a)Express the given resolution of each model in the appropriate unit in
prefix form to the nearest tenth.
b)All flat screen LCD televisions must have a resolution of at least one
megapixel. Determine which models are not a flat screen LCD television.
© Marshall Cavendish International (Singapore) Private Limited.
11. The central processing unit (CPU) in a computer executes the computer
instructions necessary to perform the designated task. 1.5 gigahertz means
that the CPU is running at 1.5 ? 109 hertz (or cycles per second).
a)Calculate how long the CPU takes to run one cycle. Express your answer in
nanoseconds. Round the coefficient to the nearest hundredth.
b)If a computer has a processing speed of 1,700 million instructions per
second, find the average number of cycles per instruction. Write your
answer to the nearest unit.
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Name: Date: Solve. Show your work.
12. The approximate diameter of a SARS virus is between 6 ? 1028 meter and
2.2 ? 1027 meter.
a)
Express the range of this diameter in prefix form using nanometers.
b)
A
virus of diameter 48 nanometers has just been detected in a small
community. Use the diameter to predict if this newly detected virus is a
SARS virus?
13. The distance between town A and town B is 10 megameters while that
between town A and town C is 100 kilometers. Is town B or town C nearer to
town A?
15. About 20,000 steel barrels were used for oil transport and storage. If each
standard barrel has a diameter of 22.5 inches and 33.5 inches in height,
how much oil is there altogether in the 20,000 steel barrels? Use 3.14 as an
approximation for p . Write your answer in scientific notation and round the
coefficient to the nearest tenth.
© Marshall Cavendish International (Singapore) Private Limited.
14. A microscopic view of two organisms, P and Q, revealed their lengths as
25 nanometers and 2,500 picometers, respectively. Which organism has the
greater length?
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12.Difference in the population served in city A
and city C
5 Population served in city A 2 Population
served in city C
5 300,200,000 2 13,100,000
5 3.002 ? 108 2 1.31 ? 107
5 30.02 ? 107 2 1.31 ? 107
5 (30.02 2 1.31) ? 107
5 28.71 ? 107
5 2.871 ? 101 ? 107
5 2.871 ? 101 1 7
5 2.871 ? 108
So, the population served in city A is
2.871 ? 108 more than the population served
in city C.
13.Total population served in the three cities
5 Population served in city A 1
Population served in city B 1
Population served in city C
5 300,200,000 1 6.4 ? 106 1 13,100,000
5 3.002 ? 108 1 6.4 ? 106 1 1.31 ? 107
5 300.2 ? 106 1 6.4 ? 106 1 13.1 ? 106
5 (300.2 1 6.4 1 13.1) ? 106
5 319.7 ? 106
5 3.197 ? 102 ? 106
5 3.197 ? 102 1 6
5 3.197 ? 108
 3.2 ? 108
So, the total population served in the three
cities is approximately 3.2 ? 108.
3.6.2 ? 105 ? 4.7 ? 1028
5 6.2 ? 4.7 ? 105 ? 1028
5 29.14 ? 105 ? 1028
5 2.914 ? 101 ? 105 ? 1028
5 2.914 ? 101 1 5 2 8
5 2.914 ? 1022
 2.9 ? 1022
4.6.8 ? 1010 4 2.3 ? 1024
© Marshall Cavendish International (Singapore) Private Limited.
3.8 103
5
5
5
5
5
 7.8 ? 1021 ? 105
5 7.8 ? 1021 1 5
5 7.8 ? 104
2
4.86 10
3.8 10 3
4.86 102
3.8
103 (2 )
4.86
3.8
103 2
4.86
3.8
105
4.86
4
2.3 10
6.8 1010
2.3 104
6.8
10 (
4 )
10
2.3
6.8
10 4
10
2.3
 3.0 1014
5. Length of Mississippi River
do River
Length of Colorad
3.860 10 3
8.94 10
2
3.860 10 3
8.94 10 2
3.86
103 2
8.94
3.86
101
8.94
3.86
10
8.94
Lesson 2.3
1.8.5 ? 1022 ? 9.52 ? 107
5 8.5 ? 9.52 ? 1022 ? 107
5 80.92 ? 1022 ? 107
5 8.092 ? 101 ? 1022 ? 107
5 8.092 ? 101 2 2 1 7
5 8.092 ? 106
 8.1 ? 106
2.3.8 ? 103 4 4.86 ? 1022
6.8 1010
 4.3
The Mississippi River has a length that is
approximately 4.3 times as great as the
length of Colorado River.
6.
Length of Rio Grande
Length of Colorado Riverr
1.885 10 3
8.94 10
2
1.885 10 3
8.94 10 2
1.885
103 2
8.94
1.885
101
8.94
1.885
10
8.94
 2.1
The Rio Grande has a length that is
approximately 2.1 times as great as the
length of the Colorado River.
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Length of Rio Grande
3.86 10 3
1.885 10 3
3.86
103 3
1.885
3.86
100
1.885
≈ 2.0

The Mississippi River has a length that is
approximately 2.0 times as great as the
length of the Rio Grande.
8. a) 12 h 5 12 ? 60 ? 60
5 43,200
5 4.32 ? 104 s
Distance
5 Speed ? Time
5 220 ? 43,200
5 2.2 ? 102 ? 4.32 ? 104
5 2.2 ? 4.32 ? 102 ? 104
5 9.504 ? 102 ? 104
5 9.504 ? 102 1 4
5 9.504 ? 106 μm
5 9.504 ? 106 ? 1026 m
5 9.504 ? 106 2 6 m
5 9.504 ? 100 m
5 9.504 m
The bacteria moved a distance of
9.504 meters.
b) Total distance
5 Number of seconds ? Distance per
second
5 5.45 ? 109 ? 8 ? 1027
5 5.45 ? 8 ? 109 ? 1027
5 43.6 ? 109 ? 1027
5 4.36 ? 101 ? 109 ? 1027
5 4.36 ? 101 1 9 2 7
5 4.36 ? 103 m
5 4.36 ? 103 ? 106 mm
5 4.36 ? 103 1 6 mm
5 4.36 ? 109 mm
The bacteria moved a distance of
4.36 ? 109 micrometers.
9. Side length of the larger cube:
8 m 5 8 ? 102 cm
Side length of the smaller cube:
3.5 m 5 3.5 ? 102 cm
a)Volume of the large cube before the
small cube is cut out
5 8 ? 102 ? 8 ? 102 ? 8 ? 102
5 8 ? 8 ? 8 ? 102 ? 102 ? 102
5 512 ? 102 ? 102 ? 102
5 5.12 ? 102 ? 102 ? 102 ? 102
5 5.12 ? 102 1 2 1 2 1 2
5 5.12 ? 108 cm3
b) Volume of the smaller cube
5 3.5 ? 102 ? 3.5 ? 102 ? 3.5 ? 102
5 3.5 ? 3.5 ? 3.5 ? 102 ? 102 ? 102
5 42.875 ? 102 ? 102 ? 102
5 4.2875 ? 101 ? 102 ? 102 ? 102
5 4.2875 ? 101 1 2 1 2 1 2
5 4.2875 ? 107 cm3
Volume of the solid left
5 Volume of the large cube 2
Volume of the smaller cube
5 5.12 ? 108 2 4.2875 ? 107
5 51.2 ? 107 2 4.2875 ? 107
5 (51.2 2 4.2875) ? 107
5 46.9125 ? 107
5 4.69125 ? 101 ? 107
 4.7 ? 101 1 7
5 4.7 ? 108 cm3
10. a) Model A:
1,280 ? 720
5 1.28 ? 103 ? 7.2 ? 102
5 1.28 ? 7.2 ? 103 ? 102
5 9.216 ? 103 ? 102
5 0.9216 ? 101 ? 103 ? 102
5 0.9216 ? 101 1 3 1 2
5 0.9216 ? 106 p
 0.9 Mp
Model B:
1,024 ? 768
5 1.024 ? 103 ? 7.68 ? 102
5 1.024 ? 7.68 ? 103 ? 102
5 7.86432 ? 103 ? 102
5 0.786432 ? 101 ? 103 ? 102
5 0.786432 ? 101 1 3 1 2
5 0.786432 ? 106 p
 0.8 Mp
Model C:
1,366 ? 768
5 1.366 ? 103 ? 7.68 ? 102
5 1.366 ? 7.68 ? 103 ? 102
5 10.49088 ? 103 ? 102
5 1.049088 ? 101 ? 103 ? 102
5 1.049088 ? 101 1 3 1 2
5 1.049088 ? 106 p
 1.0 Mp
© Marshall Cavendish International (Singapore) Private Limited.
7. Length of Mississippi River
144 Answers
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Model D:
1,920 ? 1,080
5 1.92 ? 103 ? 1.08 ? 103
5 1.92 ? 1.08 ? 103 ? 103
5 2.0736 ? 103 ? 103
5 2.0736 ? 103 1 3
5 2.0736 ? 106 p
 2.1 Mp
b)0.9216 , 1, and 0.786432 , 1
So, models A and B are not flat screen
LCD televisions.
11. a) Time taken for one cycle
1
9
1.5 10
1 100
1.5 109
1
109 s
1.5
≈ 0.67 ns

So, the CPU takes approximately
0.67 nanosecond to run one cycle.
b)In 1 second, the computer could run
1.5 ? 109 cycles and execute 1.7 ? 109
instructions.
Average number of cycles per instruction
1.5 10
9
1.7 10
9
© Marshall Cavendish International (Singapore) Private Limited.
1.5 109
1.7 109
1.5
1.7
≈1

So, there is approximately 1 cycle per
instruction.
12. a)6 ? 1028 m
5 60 ? 1021 ? 1028 m
5 60 ? 1021 2 8 m
5 60 ? 1029 m
5 60 nm
2.2 ? 1027 m
5 220 ? 1022 ? 1027 m
5 220 ? 1022 2 7 m
5 220 ? 1029 m
5 220 nm
The approximate diameter is between
60 nanometers and 220 nanometers.
b)48 nanometers is not in the range of the
diameter of a SARS virus. So, it could
not be a SARS virus.
13.Distance between towns A and B:
10 Mm 5 101 ? 106 m
5 101 1 6 m
5 107 m
Distance between towns A and C:
100 km 5 100 ? 103 m
5 1 ? 102 ? 103 m
5 102 1 3 m
5 105 m
105 , 107
So, town C is nearer to town A.
14.Length of organism P:
25 nm 5 25 ? 1029 m
5 2.5 ? 101 ? 1029 m
5 2.5 ? 101 2 9 m
5 2.5 ? 1028 m
Length of organism Q:
2,500 pm 5 2,500 ? 10212 m
5 2.5 ? 103 ? 10212 m
5 2.5 ? 103 2 12 m
5 2.5 ? 1029 m
28
10 . 1029
So, organism P has the greater length.
15.Volume of a steel barrel
5 pr2h
2


 3.14 ?  22.5  ? 33.5 in3
Volume of oil in 20,000 steel barrels


 20,000 ? 3.14 ?  22.5  ? 33.5
 2 
2
 2 
5 266,262,187.5
 2.7 ? 108 in3
There is approximately 2.7 ? 108 cubic inches
of oil.
Brain@Work
1. 1 trillion 5 1012
5 103 1 9
5 103 ? 109
5 1,000 billion
There are 1,000 billions in a trillion.
2. 72,000 trillion 5 7.2 ? 104 ? 1012
5 7.2 ? 104 1 12
5 7.2 ? 1016
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