Express each number in scientific notation.

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 ? 108

2. 1,902,500,000

SOLUTION: 1,902,500,000 1.9025000000 The decimal point moved 9 places to the left, so n = 9. 1,902,500,000 = 1.9025 ? 109

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. 0.00000804 = 8.04 ? 10?6

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 ? 1010

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. 1,500,000,000 = 1.5 ? 109

Express each number in standard form. 7. 1.98 ? 107

SOLUTION: 1.98 ? 107 has an exponent of 7, so n = 7. Move the decimal point 7 places to the right. 1.98 ? 107 = 19,800,000

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8. 4.052 ? 106

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SOLUTION: 1.5 billion = 1,500,000,000 1.5 7-4 STchieendteifciicmNaloptaoitniot nmoved 9 places to the left, so n = 9. 1,500,000,000 = 1.5 ? 109

Express each number in standard form. 7. 1.98 ? 107

SOLUTION: 1.98 ? 107 has an exponent of 7, so n = 7. Move the decimal point 7 places to the right. 1.98 ? 107 = 19,800,000

8. 4.052 ? 106 SOLUTION: 4.052 ? 106 has an exponent of 6, so n = 6. Move the decimal point 6 places to the right. 4.052 ? 106 = 4,052,000

9. 3.405 ? 10-8 SOLUTION: 3.405 ? 10?8 has an exponent of -8, so n = ?8. Move the decimal point 8 places to the left. 3.405 ? 10?8 = 0.00000003405

10. 6.8 ? 10-5 SOLUTION: 6.8 ? 10?5 has an exponent of -5, so n = ?5. Move the decimal point 5 places to the left. 6.8 ? 10?5 = 0.000068

Evaluate each product. Express the results in both scientific notation and standard form. 11. (1.2 ? 103)(1.45 ? 1012)

SOLUTION:

1,740,000,000,000,000

12. (7.08 ? 1014)(5 ? 10-9) SOLUTION:

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7-4 S1c,7ie4n0t,0if0i0c,0N0o0t,0a0t0io,0n00

12. (7.08 ? 1014)(5 ? 10-9) SOLUTION:

3,540,000 13. (5.18 ? 102)(9.1 ? 10-5)

SOLUTION:

0.047138 14. (2.18 ? 10-2)2

SOLUTION:

0.0047524 Evaluate each quotient. Express the results in both scientific notation and standard form. 15. SOLUTION:

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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.

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SOLUTION:

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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. 0.01 = 1 ? 10-2 One micron is one millionth of a millimeter. 0.000001 1.0 The decimal point moved 6 places to the left, so n = -6. 0.000001 = 1 ? 10-6 c. The filter in the purifier will stop particles as small as one hundredth of a micron or 1 ? 10-2 times the size of a micron. A micron is one millionth of a millimeter or 1 ? 10-6 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

eSolutEioxnspMreansusael a- Pcohwneruedmbby eCroginnersocientific notation. 20. 1,220,000

or 0.00000000001 m.

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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. 0.01 = 1 ? 10-2 One micron is one millionth of a millimeter. 0.000001 1.0 The decimal point moved 6 places to the left, so n = -6. 0.000001 = 1 ? 10-6 c. The filter in the purifier will stop particles as small as one hundredth of a micron or 1 ? 10-2 times the size of a micron. A micron is one millionth of a millimeter or 1 ? 10-6 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

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. 1,220,000 = 1.22 ? 106

21. 58,600,000

SOLUTION: 58,600,000 5.8600000 The decimal point moved 7 places to the left, so n = 7. 58,600,000 = 5.86 ? 107

eS2o2l.ut1io,4ns05M,a0n0u0a,l0-0P0o,0w0e0red by Cognero SOLUTION: 1,405,000,000,000 1.405000000000

or 0.00000000001 m.

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SOLUTION: 58,600,000 5.8600000 7-4 STchieendteifciicmNaloptaoitniot nmoved 7 places to the left, so n = 7. 58,600,000 = 5.86 ? 107

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. 1,405,000,000,000 = 1.405 ? 1012

23. 0.0000013

SOLUTION: 0.0000013 1.3 The decimal point moved 6 places to the right, so n = ?6. 0.0000013 = 1.3 ? 10?6

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. 0.000000000709 = 7.09 ? 10?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 ? 108

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. 5,500,000,000 = 5.5 ? 109

Express each number in standard form. 28. 1 ? 1012

SOLUTION: 1 ? 1012 has an exponent of 12, so n = 12. Move the decimal point 12 places to the right. 1 ? 1012 = 1,000,000,000,000

eS2o9l.ut9io.n4s?M1an0u7al - Powered by Cognero SOLUTION: 9.4 ? 107 has an exponent of 7, so n = 7.

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SOLUTION:

1 ? 1012 has an exponent of 12, so n = 12. Move the decimal point 12 places to the right. 7-4 S1c?ie1n0ti1f2ic=N1,o0t0a0t,i0o0n0,000,000

29. 9.4 ? 107

SOLUTION: 9.4 ? 107 has an exponent of 7, so n = 7. Move the decimal point 7 places to the right. 9.4 ? 107 = 94,000,000

30. 8.1 ? 10-3

SOLUTION: 8.1 ? 10?3 has an exponent of -3, so n = ?3. Move the decimal point 3 places to the left. 8.1 ? 10?3 = 0.0081

31. 5 ? 10-4

SOLUTION: 5 ? 10?4 has an exponent of -4, so n = ?4. Move the decimal point 4 places to the left. 5 ? 10?4 = 0.0005

32. 8.73 ? 1011

SOLUTION: 8.73 ? 1011 has an exponent of 11, so n = 11. Move the decimal point 11 places to the right. 8.73 ? 1011 = 873,000,000,000

33. 6.22 ? 10-6

SOLUTION: 6.22 ? 10?6 has an exponent of -6, so n = ?6. Move the decimal point 6 places to the left. 6.22 ? 10?6 = 0.00000622

INTERNET Express each number in standard form. 34. About 2.1 ? 107 people, aged 12 to 17, use the Internet.

SOLUTION: 2.1 ? 107 has an exponent of 7, so n = 7. Move the decimal point 7 places to the right. 2.1 ? 107 = 21,000,000

35. Approximately 1.1 ? 107 teens go online daily.

SOLUTION:

1.1 ? 107 has an exponent of 7, so n = 7. Move the decimal point 7 places to the right. eSolut1io.n1s?M1an0u7al - P1ow1,e0re0d0,b0y0C0ognero

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Evaluate each product or quotient. Express the results in both scientific notation and standard form.

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