Lesson 2.2
Adding and Subtracting in Scientific Notation: GROUP WORK
Solve. Show your work. Round the coefficient to the nearest tenth.
1. 7.8 ? 105 1 3.9 ? 106
2. 11.4 ? 1023 − 9.8 ? 1023
3. 5.6 ? 1022 1 8.6 ? 1021
4. 6.5 ? 107 − 2.8 ? 106
Use the table to answer questions 5 to 7. Round the coefficient to the nearest tenth.
The table shows the mass, in grams, of a grain of a substance.
Substances
A grain of salt
A grain of sand
A grain of rice
A grain of sugar
Mass (g)
5.85 ? 1025
6 ? 1024
2 ? 1022
6.5 ? 1022
5. Find the total mass in each combination.
a)
a grain of salt and a grain of sand
b)
a grain of rice and a grain of sugar
6. What is the difference in mass between a grain of salt and a grain of sand?
7. How much heavier/lighter is a grain of rice as compared to a grain of salt?
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8. The driving distance between Phoenix and Los Angeles is 599 kilometers. The driving
distance between Phoenix and Chicago is approximately 2.3 ? 103 kilometers.
a)
Which city is nearer to Phoenix, Los Angeles or Chicago?
If Bradley traveled from Phoenix to Los Angeles and Andy traveled from Phoenix to
Chicago, what is the difference in the distance traveled?Write your answer in scientific notation
and round the coefficient to the nearest tenth.
b)
9.
2.5 102 m
The diagram show a small ant and a large ant.
2 103 m
The length of a small ant is 2 ? 1023 meter and the length of a large ant is 2.5 ?
1022 meter.
a)
Find the difference in length of the two ants. Write your answer in scientific notation.
b) I f there is a trail of 2 small ants and 1 large ant in a straight line, find the total length of
the trail.
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Use the table to answer questions 10 to 13.
The table shows the number of public drinking water systems and
the population served in three different cities in a particular year.
A
Number of Drinking
Water Systems
52,873
B
19,400
C
87,672
City
Population Served
300,200,000
6.4 ? 106
13,100,000
10. Arrange the population served in each of the three cities in descending order.
11. Write the number of drinking water systems in each city in scientific notation by
rounding the coefficient to the nearest tenth.
12. What is the difference in the population served in city A and city C? Write your
answer in scientific notation.
13. Find the total population served in the three cities. Leave your answer in
scientific notation and round the coefficient to the nearest tenth.
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Lesson 2.2 Adding and Subtracting Scientific Notation Answer key
1. 7.8 ? 105 1 3.9 ? 106
5 7.8 ? 105 1 39 ? 105
5 (7.8 1 39) ? 105
5 46.8 ? 105
5 4.68 ? 101 ? 105
5 4.68 ? 101 1 5
5 4.68 ? 106
 4.7 ? 106
2. 11.4 ? 1023 − 9.8 ? 1023
5 (11.4 2 9.8) ? 1023
5 1.6 ? 1023
3. 5.6 ? 1022 1 8.6 ? 1021
5 0.56 ? 1021 1 8.6 ? 1021
5 (0.56 1 8.6) ? 1021
5 9.16 ? 1021
 9.2 ? 1021
4. 6.5 ? 107− 2.8 ? 106
5 65 ? 106 − 2.8 ? 106
5 (65 2 2.8) ? 106
5 62.2 ? 106
5 6.22 ? 101 ? 106
5 6.22 ? 101 1 6
5 6.22 ? 107
 6.2 ? 107
5. a) Total mass of a grain of salt and a grain
of sand
5 Mass of a grain of salt 1
Mass of a grain of sand
5 5.85 ? 1025 1 6 ? 1024
5 0.585 ? 1024 1 6 ? 1024
5 (0.585 1 6) ? 1024
5 6.585 ? 1024
 6.6 ? 1024 g
The total mass of a grain of salt and
a grain of sand is approximately
6.6 ? 1024 gram.
b) Total mass of a grain of rice and a grain
of sugar
5 Mass of a grain of rice 1
Mass of a grain of sugar
5 2 ? 1022 1 6.5 ? 1022
5 (2 1 6.5) ? 1022
5 8.5 ? 1022 g
The total mass of a grain of rice and a
grain of sugar is approximately
8.5 ? 1022 gram.
6. Difference in mass between a grain of salt
and a grain of sand
5 Mass of a grain of sand 2
Mass of a grain of salt
? 1024 2 5.85 ? 1025
65
65
? 1024 2 0.585 ? 1024
(652 0.585) ? 1024
5.415
5 ? 1024
 5.4 ? 1024 g
A grain of salt is approximately 5.4 ? 1024
gram lighter than a grain of sand.
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7.
8.
Difference in mass between a grain of salt
and a grain of rice
5 Mass of a grain of rice 2
Mass of a grain of salt
5 2 ? 1022 2 5.85 ? 1025
5 2 ? 1022 2 0.00585 ? 1022
5 (2 2 0.00585) ? 1022
5 1.99415 ? 1022
 2.0 ? 1022 g
A grain of rice is approximately 2.0 ? 1022
gram heavier as compared to a grain of salt.
a) Driving distance between Phoenix and
Los Angeles: 599 km 5 5.99 ? 102 km
Approximate driving distance between
Phoenix and Chicago: 2.3 ? 103 km
102  103
So, Los Angeles is nearer to Phoenix.
b)
Approximate difference in distance
traveled
5 Approximate driving distance
between Phoenix and Chicago 2
Driving distance between Phoenix and
Los Angeles
5 2.3 ? 103 2 5.99 ? 102
5 23 ? 102 2 5.99 ? 102
5 (23 2 5.99) ? 102
5 17.01 ? 102
5 1.701 ? 101 ? 102
5 1.701 ? 101 12
5 1.701 ? 103
 1.7 ? 103 km
So, Andy traveled approximately
1.7 ? 103 kilometers farther than Bradley.
9. a)
Difference in length of the two ants
5 Length of the large ant 2
Length of the small ant
5 2.5 ? 1022 2 2 ? 1023
5 2.5 ? 1022 2 0.2 ? 1022
5 (2.5 2 0.2) ? 1022
5 2.3 ? 1022 m
The large ant is 2.3 ? 10-2 meters
longer than a small ant.
b)
Total length of the trail formed
5 Total length of the 2 small ants 1
Length of the large ant
5 2 ? 2 ? 1023 1 2.5 ? 1022
5 4 ? 1023 1 2.5 ? 1022
5 0.4 ? 1022 1 2.5 ? 1022
5 (0.4 1 2.5) ? 1022
5 2.9 ? 1022 m
The total length of the trail formed is
2.9 ? 10-2 meters.
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Refer to the table below for answers 10 to 13.
Number of
Population Served
Drinking Water
City
(in Scientific
Systems (in
Notation)
Scientific Notation)
A
52,873
5 5.2873 ? 104
 5.3 ? 104
300,200,000
5 3.002 ? 108
B
19,400
5 1.94 ? 104
 1.9 ? 104
6.4 ? 106
C
87,672
5 8.7672 ?
104 8.8 ? 104
13,100,000
5 1.31 ? 107
10. 108 . 107 . 106
So, city A served the greatest population of
300,200,000, followed by city C with the
population of 13,100,000, and city B with the
population of 6.4 ? 106.
11. City A: Approximately 5.3 ? 104;
City B: Approximately 1.9 ? 104;
City C: Approximately 8.8 ? 104
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 16
5 3.197 ? 108
 3.2 ? 108
So, the total population served in the three
cities is approximately 3.2 ? 108.
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