−2 2
14. (2.18 × 10 )
ANSWER: 7-4 Scientific Notation
−4
4.7524 × 10 ; 0.0047524
Express each number in scientific notation.
2. 1,902,500,000
ANSWER: Evaluate each quotient. Express the results in
both scientific notation and standard form.
16. 9
1.9025 × 10
ANSWER: 14
4. 0.00000804
6.2 × 10 ; 620,000,000,000,000
ANSWER: 8.04 × 10
−6
18. MONEY Express each number in scientific notation.
6. Teens have an influence on their families’ spending
habit. They control about $1.5 billion of discretionary
income.
ANSWER: 9
ANSWER: −7
5.125 × 10 ; 0.0000005215
Express each number in scientific notation.
20. 1,220,000
ANSWER: 1.5 × 10
1.22 × 10
Express each number in standard form.
6
8. 4.052 × 10
ANSWER: 4,052,000
6
22. 1,405,000,000,000
ANSWER: 1.405 × 10
12
24. 0.000056
−5
10. 6.8 × 10
ANSWER: 0.000068
Evaluate each product. Express the results in
both scientific notation and standard form.
14
−9
12. (7.08 × 10 )(5 × 10 )
ANSWER: 6
3.54 × 10 ; 3,540,000
−2 2
14. (2.18 × 10 )
ANSWER: −4
4.7524 × 10 ; 0.0047524
Evaluate each quotient. Express the results in
both scientific notation and standard form.
ANSWER: −5
5.6 × 10
EMAIL Express each number in scientific notation.
26. Approximately 100 million emails sent to the
President are put into the National Archives.
ANSWER: 8
1 × 10
Express each number in standard form.
12
28. 1 × 10
ANSWER: 1,000,000,000,000
−3
30. 8.1 × 10
16. ANSWER: 14
6.2 × 10 ; 620,000,000,000,000
ANSWER: 0.0081
32. 8.73 × 10
11
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18. Page 1
ANSWER: 873,000,000,000
46. −3
30. 8.1 × 10
ANSWER: ANSWER: 7-4 Scientific
Notation
0.0081
32. 8.73 × 10
9
4.7 × 10 ; 4,700,000,000
−3 2
11
48. (2.3 × 10 )
ANSWER: 873,000,000,000
ANSWER: −6
5.29 × 10 ; 0.00000529
INTERNET Express each number in standard form.
7
50. 34. About 2.1 × 10 people, aged 12 to 17, use the
Internet.
ANSWER: −5
ANSWER: 21,000,000
2.5 × 10 ; 0.000025
52. Evaluate each product or quotient. Express the
results in both scientific notation and standard
form.
3
2
36. (3.807 × 10 )(5 × 10 )
ANSWER: 6
1.9035 × 10 ; 1,903,500
38. ANSWER: 8
2.4 × 10 ; 240,000,000
−18
40. (9.5 × 10
9
)(9 × 10 )
ANSWER: 10
4.3 × 10 ; 43,000,000,000
54. ASTRONOMY The distance between Earth and
the Sun varies throughout the year. Earth is closest to
the Sun in January when the distance is 91.4 million
miles. In July, the distance is greatest at 94.4 million
miles.
a. Write 91.4 million in both standard form and in
scientific notation.
b. Write 94.4 million in both standard form and in
scientific notation.
c. What is the percent increase in distance from
January to July? Round to the nearest tenth of a
percent.
ANSWER: ANSWER: ; 0.0000000855
a. 91,400,000; 9.14 × 107
7
b. 94,400,000; 9.44 × 10
c. 3.3%
42. ANSWER: Evaluate each product or quotient. Express the
results in both scientific notation and standard
form.
−4
1.5 × 10 ; 0.00015
2
6
44. (2.58 × 10 )(3.6 × 10 )
56. ANSWER: ANSWER: 8
9.288 × 10 ; 928,800,000
6
9.1 × 10 ; 9,100,000
46. −2 2
58. (3.16 × 10 )
ANSWER: ANSWER: 9
-4
4.7 × 10 ; 4,700,000,000
9.9856 × 10 ; 0.0099856
−3 2
48. (2.3 × 10 )
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ANSWER: −6
5.29 × 10 ; 0.00000529
Page 2
60. ANSWER: watershed as the Mississippi River watershed?
−2 2
58. (3.16 × 10 )
ANSWER: 6
ANSWER: 7-4 Scientific Notation
-4
9.9856 × 10 ; 0.0099856
6
a. 2.3 × 10 ; 1.2 × 10
b. about 1.9 times as large
10
70. REASONING Which is greater, 100
Explain your reasoning.
60. 100
or 10
?
ANSWER: ANSWER: 10
−9
2 10
100 = (10 )
10
100
7.2 × 10 ; 0.0000000072
62. 20
or 10
100
and 10
20
> 10 , so 10
100
>
72. CHALLENGE Order these numbers from least to
greatest without converting them to standard form.
−3
ANSWER: 0
1.2 × 10 ; 1.2
LIGHT The speed of light is approximately 3 ×
8
10 meters per second.
64. Write an expression to represent the speed of light in
kilometers per hour.
−4
4
−3
ANSWER: 5
7.95 × 10 bits of data every second. Company B’s
6
phone processes up to 1.41 × 10 bits of data every
second. Evaluate and interpret
.
ANSWER: about 1.774
The phone from company B is about 1.774 times as
fast as the phone from company A.
68. RIVERS A drainage basin separated from adjacent
basins by a ridge, hill, or mountain, is known as a
watershed. The watershed of the Amazon River is
2,300,000 square miles. The watershed of the
Mississippi River is 1,200,000 square miles.
a. Write each of these numbers in scientific notation.
b. How many times as large is the Amazon River
watershed as the Mississippi River watershed?
6
a. 2.3 × 10 ; 1.2 × 10
b. about 1.9 times as large
70. REASONING Which is greater, 100
Explain your reasoning.
20
ANSWER: C
78. SHORT RESPONSE In his first four years of
coaching football, Coach Delgato’s team won 5
games the first year, 10 games the second year, 8
games the third year, and 7 games the fourth year.
How many games does the team need to win during
the fifth year to have an average of 8 wins per year?
10
80. HEALTH A ponderal index p is a measure of a
person’s body based on height h in centimeters and
mass m in kilograms. 100
or 10
?
ANSWER: eSolutions
Manual - Powered by Cognero
or 10
76. Which number represents 0.05604 × 10 written in
standard form?
A 0.0000000005604
B 560,400
C 5,604,000
D 50,604,000
ANSWER: 10 games
ANSWER: 6
−9
5
Sample answer: product: 2.5 × 10 , 5.2 × 10 ;
3
6
quotient: 2.6 × 10 , 2 × 10
8
.
2 10
5
−4.65 × 10 , −5.64 × 10 , 4.56 × 10 , 5.46 × 10 ,
3
6.54 × 10
−3
66. CCSS MODELING A recent cell phone study
showed that company A’s phone processes up to
10
ANSWER: notation with a product of 1.3 × 10 . Then name
two numbers in scientific notation with a quotient of
−3
1.3 × 10 .
9
100 = (10 )
10
100
4
74. OPEN ENDED Write two numbers in scientific
ANSWER: 1.08 × 10
−4
3
5.46 × 10 , 6.54 × 10 , 4.56 × 10 , −5.64 × 10 ,
5
−4.65 × 10
100
and 10
20
> 10 , so 10
100
>
One such formula is
.
If a person who is 182 centimeters tall has a ponderal
Page 3
index of about 2.2, how much does the person weigh
in kilograms?
How many games does the team need to win during
the fifth year to have an average of 8 wins per year?
ANSWER: 7-4 Scientific
Notation
10 games
80. HEALTH A ponderal index p is a measure of a
person’s body based on height h in centimeters and
mass m in kilograms. One such formula is
.
If a person who is 182 centimeters tall has a ponderal
index of about 2.2, how much does the person weigh
in kilograms?
ANSWER: 64.2 kg
Simplify. Assume that no denominator is equal
to zero.
82. ANSWER: 2
6 or 36
84. ANSWER: 86. ANSWER: x
Evaluate a(b ) for each of the given values.
88. a = 1, b = 2, x = 4
ANSWER: 16
90. a = 5, b = 3, x = 0
ANSWER: 5
92. a = –2, b = 3, x = 1
ANSWER: –6
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