7-4 Scientific Notation
Express each number in scientific notation.
1. 185,000,000
SOLUTION: 185,000,000 → 1.85000000
The decimal point moved 8 places to the left, so n = 8.
185,000,000 = 1.85 × 10
8
2. 1,902,500,000
SOLUTION: 1,902,500,000 → 1.9025000000
The decimal point moved 9 places to the left, so n = 9.
9
1,902,500,000 = 1.9025 × 10
3. 0.000564
SOLUTION: 0.000564 → 5.64
The decimal point moved 4 places to the right, so n = –4.
0.000564 = 5.64 × 10
–4
4. 0.00000804
SOLUTION: 0.00000804 → 8.04
The decimal point moved 6 places to the right, so n = –6.
–6
0.00000804 = 8.04 × 10
MONEY Express each number in scientific notation.
5. Teens spend $13 billion annually on clothing.
SOLUTION: 13 billion = 13,000,000,000 → 1.3
The decimal point moved 10 places to the left, so n = 10.
13,000,000,000 = 1.3 × 10
10
6. Teens have an influence on their families’ spending habit. They control about $1.5 billion of discretionary income.
SOLUTION: 1.5 billion = 1,500,000,000 → 1.5
The decimal point moved 9 places to the left, so n = 9.
9
1,500,000,000 = 1.5 × 10
Express each number in standard form.
7. 1.98 × 10
7
SOLUTION: 7
1.98 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
1.98 × 10 = 19,800,000
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8. 4.052 × 10
6
Page 1
SOLUTION: 1.5 billion = 1,500,000,000 → 1.5
The decimal
point moved 9 places to the left, so n = 9.
7-4 Scientific
Notation
9
1,500,000,000 = 1.5 × 10
Express each number in standard form.
7. 1.98 × 10
7
SOLUTION: 7
1.98 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
1.98 × 10 = 19,800,000
8. 4.052 × 10
6
SOLUTION: 6
4.052 × 10 has an exponent of 6, so n = 6.
Move the decimal point 6 places to the right.
6
4.052 × 10 = 4,052,000
9. 3.405 × 10
−8
SOLUTION: –8
3.405 × 10 has an exponent of −8, so n = –8.
Move the decimal point 8 places to the left.
3.405 × 10
–8
= 0.00000003405
−5
10. 6.8 × 10
SOLUTION: –5
6.8 × 10 has an exponent of −5, so n = –5.
Move the decimal point 5 places to the left.
–5
6.8 × 10 = 0.000068
Evaluate each product. Express the results in both scientific notation and standard form.
3
12
11. (1.2 × 10 )(1.45 × 10 )
SOLUTION: 1,740,000,000,000,000
14
−9
12. (7.08 × 10 )(5 × 10 )
SOLUTION: eSolutions Manual - Powered by Cognero
Page 2
7-4 Scientific
Notation
1,740,000,000,000,000
14
−9
12. (7.08 × 10 )(5 × 10 )
SOLUTION: 3,540,000
2
−5
13. (5.18 × 10 )(9.1 × 10 )
SOLUTION: 0.047138
−2 2
14. (2.18 × 10 )
SOLUTION: 0.0047524
Evaluate each quotient. Express the results in both scientific notation and standard form.
15. SOLUTION: eSolutions Manual - Powered by Cognero
Page 3
7-4 Scientific Notation
0.0047524
Evaluate each quotient. Express the results in both scientific notation and standard form.
15. SOLUTION: 4,500
16. SOLUTION: 620,000,000,000,000
17. SOLUTION: 0.00000000000085
18. eSolutions Manual - Powered by Cognero
SOLUTION: Page 4
7-4 Scientific Notation
0.00000000000085
18. SOLUTION: 0.0000005125
19. CCSS PRECISION Salvador bought an air purifier to help him deal with his allergies. The filter in the purifier will
stop particles as small as one hundredth of a micron. A micron is one millionth of a millimeter.
a. Write one hundredth and one micron in standard form.
b. Write one hundredth and one micron in scientific notation.
c. What is the smallest size particle in meters that the filter will stop? Write the result in both standard form and
scientific notation.
SOLUTION: a. 0.01, 0.000001
b. 0.01 → 1.0
The decimal point moved 2 places to the right, so n = −2.
−2
0.01 = 1 × 10
One micron is one millionth of a millimeter.
0.000001 → 1.0
The decimal point moved 6 places to the left, so n = −6.
−6
0.000001 = 1 × 10
−2
c. The filter in the purifier will stop particles as small as one hundredth of a micron or 1 × 10 times the size of a
−6
micron. A micron is one millionth of a millimeter or 1 × 10 times the size of a millimeter. Multiply to find the
smallest size particle in millimeters that the filter will stop.
Since the question asked for the smallest size particle in meters that the filter will stop, and 1,000 millimeters = 1
meter, use dimensional analysis to write
in meters.
So, the smallest size particle in meters that the filter will stop is
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Express each number in scientific notation.
20. 1,220,000
or 0.00000000001 m.
Page 5
7-4 Scientific Notation
0.0000005125
19. CCSS PRECISION Salvador bought an air purifier to help him deal with his allergies. The filter in the purifier will
stop particles as small as one hundredth of a micron. A micron is one millionth of a millimeter.
a. Write one hundredth and one micron in standard form.
b. Write one hundredth and one micron in scientific notation.
c. What is the smallest size particle in meters that the filter will stop? Write the result in both standard form and
scientific notation.
SOLUTION: a. 0.01, 0.000001
b. 0.01 → 1.0
The decimal point moved 2 places to the right, so n = −2.
−2
0.01 = 1 × 10
One micron is one millionth of a millimeter.
0.000001 → 1.0
The decimal point moved 6 places to the left, so n = −6.
−6
0.000001 = 1 × 10
−2
c. The filter in the purifier will stop particles as small as one hundredth of a micron or 1 × 10 times the size of a
−6
micron. A micron is one millionth of a millimeter or 1 × 10 times the size of a millimeter. Multiply to find the
smallest size particle in millimeters that the filter will stop.
Since the question asked for the smallest size particle in meters that the filter will stop, and 1,000 millimeters = 1
meter, use dimensional analysis to write
in meters.
So, the smallest size particle in meters that the filter will stop is
or 0.00000000001 m.
Express each number in scientific notation.
20. 1,220,000
SOLUTION: 1,220,000 → 1.220000
The decimal point moved 6 places to the left, so n = 6.
6
1,220,000 = 1.22 × 10
21. 58,600,000
SOLUTION: 58,600,000 → 5.8600000
The decimal point moved 7 places to the left, so n = 7.
7
58,600,000 = 5.86 × 10
22. 1,405,000,000,000
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SOLUTION: 1,405,000,000,000 → 1.405000000000
Page 6
SOLUTION: 58,600,000 → 5.8600000
The decimal
point moved 7 places to the left, so n = 7.
7-4 Scientific
Notation
7
58,600,000 = 5.86 × 10
22. 1,405,000,000,000
SOLUTION: 1,405,000,000,000 → 1.405000000000
The decimal point moved 12 places to the left, so n = 12.
12
1,405,000,000,000 = 1.405 × 10
23. 0.0000013
SOLUTION: 0.0000013 → 1.3
The decimal point moved 6 places to the right, so n = –6.
–6
0.0000013 = 1.3 × 10
24. 0.000056
SOLUTION: 0.000056 → 5.6
The decimal point moved 5 places to the right, so n = –5.
0.000056 = 5.6 × 10
–5
25. 0.000000000709
SOLUTION: 0.000000000709 → 7.09
The decimal point moved 10 places to the right, so n = –10.
–10
0.000000000709 = 7.09 × 10
EMAIL Express each number in scientific notation.
26. Approximately 100 million emails sent to the President are put into the National Archives.
SOLUTION: 100 million = 100,000,000 → 1.0
The decimal point moved 7 places to the left, so n = 8.
100,000,000 = 1.0 × 10
8
27. By 2010, the email security market will generate $5.5 billion.
SOLUTION: 5.5 billion = 5,500,000,000 → 5.5
The decimal point moved 9 places to the left, so n = 9.
9
5,500,000,000 = 5.5 × 10
Express each number in standard form.
12
28. 1 × 10
SOLUTION: 12
1 × 10 has an exponent of 12, so n = 12.
Move the decimal point 12 places to the right.
12
1 × 10
= 1,000,000,000,000
7
29. 9.4 × 10
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SOLUTION: 7
9.4 × 10 has an exponent of 7, so n = 7.
Page 7
SOLUTION: 12
1 × 10 has an exponent of 12, so n = 12.
Move the decimal point 12 places to the right.
12
7-4 Scientific
1 × 10 =Notation
1,000,000,000,000
7
29. 9.4 × 10
SOLUTION: 7
9.4 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
9.4 × 10 = 94,000,000
−3
30. 8.1 × 10
SOLUTION: –3
8.1 × 10 has an exponent of −3, so n = –3.
Move the decimal point 3 places to the left.
–3
8.1 × 10
= 0.0081
−4
31. 5 × 10
SOLUTION: –4
5 × 10 has an exponent of −4, so n = –4.
Move the decimal point 4 places to the left.
–4
5 × 10 = 0.0005
32. 8.73 × 10
11
SOLUTION: 11
8.73 × 10 has an exponent of 11, so n = 11.
Move the decimal point 11 places to the right.
8.73 × 10
33. 6.22 × 10
11
= 873,000,000,000
−6
SOLUTION: –6
6.22 × 10 has an exponent of −6, so n = –6.
Move the decimal point 6 places to the left.
–6
6.22 × 10 = 0.00000622
INTERNET Express each number in standard form.
7
34. About 2.1 × 10 people, aged 12 to 17, use the Internet.
SOLUTION: 7
2.1 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
2.1 × 10 = 21,000,000
7
35. Approximately 1.1 × 10 teens go online daily.
SOLUTION: 7
1.1 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
1.1 × 10
→ 11,000,000
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Manual
- Powered by Cognero
Evaluate each product or quotient. Express the results in both scientific notation and standard form.
3
2
Page 8
SOLUTION: 7
2.1 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
7-4 Scientific
2.1 × 10 =Notation
21,000,000
7
35. Approximately 1.1 × 10 teens go online daily.
SOLUTION: 7
1.1 × 10 has an exponent of 7, so n = 7.
Move the decimal point 7 places to the right.
7
1.1 × 10 → 11,000,000
Evaluate each product or quotient. Express the results in both scientific notation and standard form.
3
2
36. (3.807 × 10 )(5 × 10 )
SOLUTION: 1,903,500
37. SOLUTION: 80,000,000
38. SOLUTION: 240,000,000
7
−2
39. (6.5 × 10 )(7.2 × 10 )
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Page 9
7-4 Scientific Notation
240,000,000
−2
7
39. (6.5 × 10 )(7.2 × 10 )
SOLUTION: 4,680,000
−18
40. (9.5 × 10
9
)(9 × 10 )
SOLUTION: 0.0000000855
41. SOLUTION: 22,000,000
42. SOLUTION: 0.00015
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6 -2Powered by Cognero
43. (1.4 × 10 )
SOLUTION: Page 10
7-4 Scientific Notation
22,000,000
42. SOLUTION: 0.00015
6 2
43. (1.4 × 10 )
SOLUTION: 1,960,000,000,000
2
6
44. (2.58 × 10 )(3.6 × 10 )
SOLUTION: 928,800,000
45. SOLUTION: 689,000
46. eSolutions
Manual - Powered by Cognero
SOLUTION: Page 11
7-4 Scientific Notation
689,000
46. SOLUTION: 4,700,000,000
–7
3
47. (5 × 10 )(1.8 × 10 )
SOLUTION: 0.0009
−3 2
48. (2.3 × 10 )
SOLUTION: 0.00000529
49. SOLUTION: 0.000005
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SOLUTION: Page 12
7-4 Scientific Notation
0.000005
50. SOLUTION: 0.000025
7 2
51. (7.2 × 10 )
SOLUTION: 5,184,000,000,000
52. SOLUTION: 43,000,000,000
−5 2
53. (6.3 × 10 )
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Page 13
7-4 Scientific Notation
43,000,000,000
−5 2
53. (6.3 × 10 )
SOLUTION: 0.000000003969
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.
SOLUTION: a. 91.4 million = 91,400,000 → 9.14
The decimal point moved 7 places to the left, so n = 7.
7
91,400,000 = 9.14 × 10
b. 94.4 million = 94,400,000 → 9.44
The decimal point moved 7 places to the left, so n = 7.
7
94,400,000 = 9.44 × 10
c. Percent increase is the amount of increase divided by the original quantity.
So, the percent increase is about 3.3%.
Evaluate each product or quotient. Express the results in both scientific notation and standard form.
−2
6
55. (4.65 × 10 )(5 × 10 )
SOLUTION: eSolutions Manual - Powered by Cognero
232,500
Page 14
7-4 Scientific Notation
So, the percent increase is about 3.3%.
Evaluate each product or quotient. Express the results in both scientific notation and standard form.
−2
6
55. (4.65 × 10 )(5 × 10 )
SOLUTION: 232,500
56. SOLUTION: 9,100,000
57. SOLUTION: 0.000000061
−2 2
58. (3.16 × 10 )
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Page 15
7-4 Scientific Notation
0.000000061
−2 2
58. (3.16 × 10 )
SOLUTION: 0.00099856
−4
−3
59. (2.01 × 10 )(8.9 × 10 )
SOLUTION: 0.0000017889
60. SOLUTION: 0.0000000072
6
−4
61. (9.04 × 10 )(5.2 × 10 )
SOLUTION: eSolutions Manual - Powered by Cognero
Page 16
7-4 Scientific Notation
0.0000000072
6
−4
61. (9.04 × 10 )(5.2 × 10 )
SOLUTION: 4700.8
62. SOLUTION: 1.2
LIGHT The speed of light is approximately 3 × 108 meters per second.
63. Write an expression to represent the speed of light in kilometers per second.
SOLUTION: 64. Write an expression to represent the speed of light in kilometers per hour.
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65. Make a table to show how many kilometers light travels in a day, a week, a 30-day month, and a 365-day year.
Page 17
7-4 Scientific Notation
64. Write an expression to represent the speed of light in kilometers per hour.
SOLUTION: 65. Make a table to show how many kilometers light travels in a day, a week, a 30-day month, and a 365-day year.
Express your results in scientific notation.
SOLUTION: For 1 day:
For 1 week:
For 1 month:
For 1 year:
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5 Page 18
66. CCSS MODELING A recent cell phone study showed that company A’s phone processes up to 7.95 × 10 bits of
6
data every second. Company B’s phone processes up to 1.41 × 10 bits of data every second. Evaluate and interpret
7-4 Scientific Notation
5
66. CCSS MODELING A recent cell phone study showed that company A’s phone processes up to 7.95 × 10 bits of
6
data every second. Company B’s phone processes up to 1.41 × 10 bits of data every second. Evaluate and interpret
.
.
SOLUTION: The phone from company B is about 1.774 times as fast as the phone from company A.
9
8
67. EARTH The population of Earth is about 6.623 × 10 . The land surface of Earth is 1.483 × 10 square kilometers.
What is the population density for the land surface area of Earth?
SOLUTION: The population density is the population divided by the surface area.
So, the population density is about 44.7 persons per square kilometer.
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?
SOLUTION: a. 2,300,000 → 2.300000
The decimal point moved 6 places to the left, so n = 6.
6
2,300,000 = 2.3 × 10
1,200,000 → 1.200000
The decimal point moved 6 places to the left, so n = 6.
6
1,200,000 = 1.2 × 10
b. Divide the area of Amazon River watershed by the area of the Mississippi River watershed.
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Page 19
7-4 Scientific Notation
So, the population density is about 44.7 persons per square kilometer.
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?
SOLUTION: a. 2,300,000 → 2.300000
The decimal point moved 6 places to the left, so n = 6.
6
2,300,000 = 2.3 × 10
1,200,000 → 1.200000
The decimal point moved 6 places to the left, so n = 6.
6
1,200,000 = 1.2 × 10
b. Divide the area of Amazon River watershed by the area of the Mississippi River watershed.
So, the Amazon River watershed is about 1.9 times as large as the Mississippi River watershed.
69. AGRICULTURE In a recent year, farmers planted approximately 92.9 million acres of corn. They also planted
64.1 million acres of soybeans and 11.1 million acres of cotton.
a. Write each of these numbers in scientific notation and in standard form.
b. How many times as much corn was planted as soybeans? Write your results in standard form and in scientific
notation. Round your answer to four decimal places.
c. How many times as much corn was planted as cotton? Write your results in standard form and in scientific
notation. Round your answer to four decimal places.
SOLUTION: a. Corn: 92.9 million = 92,900,000 → 9.2900000
The decimal point moved 7 places, so n = 7.
7
92,900,000 = 9.29 × 10
Soybeans: 64.1 million = 64,100,000 → 6.4100000
The decimal point moved 7 places, so n = 7.
7
64,100,000 = 6.41 × 10
Cotton: 11.1 million = 11,100,000 → 1.1100000
The decimal point moved 7 places, so n = 7.
7
11,100,000 = 1.11 × 10
b. Divide the amount of corn planted by the amount of soybeans planted.
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So, there was about 1.4493 times more corn planted than soybeans.
c. Divide the amount of corn planted by the amount of cotton planted.
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7-4 Scientific Notation
So, the Amazon River watershed is about 1.9 times as large as the Mississippi River watershed.
69. AGRICULTURE In a recent year, farmers planted approximately 92.9 million acres of corn. They also planted
64.1 million acres of soybeans and 11.1 million acres of cotton.
a. Write each of these numbers in scientific notation and in standard form.
b. How many times as much corn was planted as soybeans? Write your results in standard form and in scientific
notation. Round your answer to four decimal places.
c. How many times as much corn was planted as cotton? Write your results in standard form and in scientific
notation. Round your answer to four decimal places.
SOLUTION: a. Corn: 92.9 million = 92,900,000 → 9.2900000
The decimal point moved 7 places, so n = 7.
7
92,900,000 = 9.29 × 10
Soybeans: 64.1 million = 64,100,000 → 6.4100000
The decimal point moved 7 places, so n = 7.
7
64,100,000 = 6.41 × 10
Cotton: 11.1 million = 11,100,000 → 1.1100000
The decimal point moved 7 places, so n = 7.
7
11,100,000 = 1.11 × 10
b. Divide the amount of corn planted by the amount of soybeans planted.
So, there was about 1.4493 times more corn planted than soybeans.
c. Divide the amount of corn planted by the amount of cotton planted.
So, there was about 8.3694 times more corn planted than cotton.
70. REASONING Which is greater, 100
10
100
or 10
? Explain your reasoning.
SOLUTION: 10
100
2 10
= (10 )
20
or 10
100
and 10
20
> 10 , so 10
100
10
> 100
71. ERROR ANALYSIS Syreeta and Pete are solving a division problem with scientific notation. Is either of them
correct? Explain your reasoning.
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70. REASONING Which is greater, 100
10
100
or 10
? Explain your reasoning.
SOLUTION: 7-4 Scientific Notation
10
2 10
20
100
20
100
10
100 = (10 ) or 10 and 10 > 10 , so 10 > 100
71. ERROR ANALYSIS Syreeta and Pete are solving a division problem with scientific notation. Is either of them
correct? Explain your reasoning.
SOLUTION: Pete is correct.
In step 4, Syreeta moved the decimal point in the wrong direction. 72. CHALLENGE Order these numbers from least to greatest without converting them to standard form.
−3
3
−4
4
5.46 × 10 , 6.54 × 10 , 4.56 × 10 , −5.64 × 10 , −4.65 × 10
5
SOLUTION: The numbers are all in standard form and all of the exponents are different, so we can compare the numbers by
analyzing the exponents. The least number is the negative number with the greatest exponent of 10. The other
negative number would come next. To order the positive numbers, order their exponents from least to greatest.
5
4
3
−4
−3
−4.65 × 10 , −5.64 × 10 , 4.56 × 10 , 5.46 × 10 , 6.54 × 10
73. CCSS ARGUMENTS Determine whether the statement is always, sometimes, or never true. Give examples or a
counterexample to verify your reasoning.
When multiplying two numbers written in scientific notation, the resulting number can have no more than two
digits to the left of the decimal point.
SOLUTION: m
n
Sample answer: Always; if the numbers are a × 10 and b × 10 in scientific notation, then 1 ≤ a < 10 and 1 ≤ b <
10. So 1 ≤ ab < 100.
−3
74. OPEN ENDED Write two numbers in scientific notation with a product of 1.3 × 10 . Then name two numbers in
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−3
scientific notation with a quotient of 1.3 × 10 .
SOLUTION: Page 22
digits to the left of the decimal point.
SOLUTION: m
n
Sample answer:
Always; if the numbers are a × 10 and b × 10 in scientific notation, then 1 ≤ a < 10 and 1 ≤ b <
7-4 Scientific
Notation
10. So 1 ≤ ab < 100.
−3
74. OPEN ENDED Write two numbers in scientific notation with a product of 1.3 × 10 . Then name two numbers in
−3
scientific notation with a quotient of 1.3 × 10 .
SOLUTION: n
m
Sample answer: Let the two numbers in scientific notation be given by a × 10 and b × 10 .
-3
If the product is to be 1.3 × 10 , then choose numbers for a and b such that ab = 13 and 1 ≤ a < 10 and 1 ≤ b < 10.
-3
-4
Select integers for n and m such that n + m = –4, since 1.3 × 10 = 13 × 10 . Since 2.5 × 5.2 = 13 and 5 + (–9) = –
−9
5
4, let the numbers be 2.5 × 10 and 5.2 × 10 . Find the product to check.
-3
−9
5
So, two numbers in scientific notation that have a product of 1.3 × 10 could be 2.5 × 10 and 5.2 × 10 .
-3
If the quotient is to be 1.3 × 10 , then choose numbers for a and b such that = 1.3 and 1 ≤ a < 10 and 1 ≤ b < 10.
3
Select integers for n and m such that n – m = –3. Since 2.6 ÷ 2 = 1.3 and 3 – 6 = –3, let the numbers be 2.6 × 10
6
and 2 × 10 . Find the quotient to check.
-3
3
6
So, two numbers in scientific notation that have a quotient of 1.3 × 10 could be 2.6 × 10 and 2 × 10 .
75. WRITING IN MATH Write the steps that you would use to divide two numbers written in scientific notation.
Then describe how you would write the results in standard form. Demonstrate by finding
3
for a = 2 × 10 and b =
5
4 × 10 .
SOLUTION: Sample answer: Divide the numbers to the left of the × symbols. Then divide the powers of 10. If necessary, rewrite the results in scientific notation. To convert that to standard form, check to see if the exponent is positive or negative.
If positive, move the decimal point to the right, and if negative, to the left. The number of places to move the decimal
point is the absolute value of the exponent. Fill in with zeros as needed.
For example:
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Page 23
8
76. Which number represents 0.05604 × 10 written in standard form?
A 0.0000000005604
7-4 Scientific
Notation
-3
3
6
So, two numbers in scientific notation that have a quotient of 1.3 × 10 could be 2.6 × 10 and 2 × 10 .
75. WRITING IN MATH Write the steps that you would use to divide two numbers written in scientific notation.
Then describe how you would write the results in standard form. Demonstrate by finding
3
for a = 2 × 10 and b =
5
4 × 10 .
SOLUTION: Sample answer: Divide the numbers to the left of the × symbols. Then divide the powers of 10. If necessary, rewrite the results in scientific notation. To convert that to standard form, check to see if the exponent is positive or negative.
If positive, move the decimal point to the right, and if negative, to the left. The number of places to move the decimal
point is the absolute value of the exponent. Fill in with zeros as needed.
For example:
8
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
SOLUTION: The exponent is 8, which means that the decimal point should be moved to the right. This means that choice A can be eliminated. When you move the decimal point 8 spaces to the right you obtain 5,604,000, so C is the correct choice.
77. Toni left school and rode her bike home. The graph below shows the relationship between her distance from the
school and time.
Which explanation could account for the section of the graph from t = 30 to t = 40?
F Toni rode her bike down a hill.
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G Toni ran all the way home.
H Toni stopped at a friend’s house on her way home.
J Toni returned to school to get her mathematics book.
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7-4 Scientific Notation
When you move the decimal point 8 spaces to the right you obtain 5,604,000, so C is the correct choice.
77. Toni left school and rode her bike home. The graph below shows the relationship between her distance from the
school and time.
Which explanation could account for the section of the graph from t = 30 to t = 40?
F Toni rode her bike down a hill.
G Toni ran all the way home.
H Toni stopped at a friend’s house on her way home.
J Toni returned to school to get her mathematics book.
SOLUTION: Going down a hill and running all the way home would both show a change in distance, so options F and
G, respectively, do not work. If she returned to school, the distance would actually go down and we would
expect the graph to show that (and it does not). So, option J does not work either.
Toni’s distance remains the same from time t = 30 to t = 40. This means that she did not move during this time, so
choice H is the correct choice.
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?
SOLUTION: Let x represent the number of wins in the fifth year.
So, Coach Delgato needs to win 10 games in his fifth year to have an average of 8 wins per year.
79. The table shows the relationship between Calories and grams of fat contained in an order of fried chicken from
various restaurants.
Assuming that the data can best be described by a linear model, how many grams of fat would you expect to be in a
275-Calorie order of fried chicken?
A 22
B 25
C 28
D 30
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SOLUTION: Find the slope between two points.
7-4 Scientific Notation
So, Coach Delgato needs to win 10 games in his fifth year to have an average of 8 wins per year.
79. The table shows the relationship between Calories and grams of fat contained in an order of fried chicken from
various restaurants.
Assuming that the data can best be described by a linear model, how many grams of fat would you expect to be in a
275-Calorie order of fried chicken?
A 22
B 25
C 28
D 30
SOLUTION: Find the slope between two points.
Now find the y–intercept using one of the points.
So, to find the fat grams for a 275-Calorie order of fried chicken, substitute 275 for x.
The answer obtained is closest to 25, so the correct choice is B.
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?
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Replace p with 2.2 and h with 182 in the formula to determine the value of m.
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7-4 Scientific
Notation
The answer obtained is closest to 25, so the correct choice is B.
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?
SOLUTION: Replace p with 2.2 and h with 182 in the formula to determine the value of m.
So, the person will weigh about 64.2 kilograms.
Simplify. Assume that no denominator is equal to zero.
81. SOLUTION: 82. SOLUTION: 83. SOLUTION: eSolutions Manual - Powered by Cognero
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7-4 Scientific Notation
83. SOLUTION: 84. SOLUTION: 85. SOLUTION: 86. eSolutions
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SOLUTION: Page 28
7-4 Scientific Notation
86. SOLUTION: 2
3
87. CHEMISTRY Lemon juice is 10 times as acidic as tomato juice. Tomato juice is 10 times as acidic as egg
whites. How many times as acidic is lemon juice as egg whites?
SOLUTION: 5
Lemon juice is 10 times more acidic than egg whites.
x
Evaluate a(b ) for each of the given values.
88. a = 1, b = 2, x = 4
SOLUTION: 89. a = 4, b = 1, x = 7
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7-4 Scientific Notation
89. a = 4, b = 1, x = 7
SOLUTION: 90. a = 5, b = 3, x = 0
SOLUTION: 91. a = 0, b = 6, x = 8
SOLUTION: 92. a = –2, b = 3, x = 1
SOLUTION: 93. a = –3, b = 5, x = 2
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