Using Scientific Notation
Page 1 of 4
Scientific Notation BEFORE
Now
WHY?
You multiplied whole numbers by powers of 10.
You’ll read and write numbers using scientific notation.
So you can compare the masses of Mars’s moons, as in Example 3.
In the Real World
Word Watch scientific notation, p. 74
Models Joseph King constructed a 23 foot model of the Eiffel Tower using 110,000 toothpicks. How can you use powers of 10 to write 110,000? One way to write large numbers is to use scientific notation.
Using Scientific Notation A number is written in scientific notation if it has the form c 10n where c is greater than or equal to 1 and less than 10 and n is a whole number. Standard form
Product form
Scientific notation
2,860,000
2.86 1,000,000
2.86 106
EXAMPLE
with
Vocabulary
Powers of ten: 101 10 102 100 103 1000 104 10,000 105 100,000 106 1,000,000
74
Chapter 2
1
Writing Numbers in Scientific Notation
As described above, Joseph King used 110,000 toothpicks to construct his Eiffel Tower model. To write 110,000 in scientific notation, use powers of 10. Standard form
Product form
Scientific notation
110,000
1.1 100,000
1.1 105
5 decimal places
5 zeros
Exponent is 5.
ANSWER Joseph King used 1.1 105 toothpicks to make his model of the Eiffel Tower.
Decimal Operations
Page 2 of 4
EXAMPLE
with
Reading
You read 7 103 as “seven times ten raised to the third power,” or “seven times ten cubed.”
2
Writing Numbers in Standard Form
Write the number in standard form. a. 7 103
b. 4.398 108
Solution Scientific notation a. 7 103 8
b. 4.398 10
Your turn now
Product form
Standard form
7 1000
7000
4.398 100,000,000
439,800,000
Write the number in scientific notation.
1. 450,000
2. 6,310,000
3. 10,000,000,000
Write the number in standard form. 4. 3.71 104
EXAMPLE
Astronomy
3
5. 9 107
6. 4.652 1010
Comparing Numbers in Scientific Notation
Mars Mars has two moons, Phobos and Deimos. Phobos has a mass of 1.06 1016 kilograms. Deimos has a mass of 2.4 1015 kilograms. Which moon has the greater mass? Solution To compare numbers written in scientific notation, first compare the exponents. If the exponents are equal, then compare the decimal parts. Phobos: 1.06 1016
Deimos: 2.4 1015
Because 16 > 15, 1.06 1016 > 2.4 1015. ■
Mars Mars is the fourth planet from the Sun. The distance between Mars and the Sun is about 1.416 108 miles. How can you write this distance in standard form?
ANSWER Phobos has a greater mass than Deimos.
✓Check
Write the numbers in standard form and compare.
1.06 1016 10,600,000,000,000,000 2.4 1015 2,400,000,000,000,000 So, 1.06 1016 > 2.4 1015.
Your turn now
Copy and complete the statement using < , >, or .
7. 9.74 1021 _?_ 2.1 1022
8. 5.28 1012 _?_ 5.3 1012
Lesson 2.5
Scientific Notation
75
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus CLASSZONE.COM
More Practice, p. 706
Getting Ready to Practice Vocabulary Tell whether the number is written in scientific notation, standard form, or neither. If neither, explain why. 1. 7.2 104
2. 34.2 105
3. 70,231
Write the number in scientific notation. 4. 75,000
5. 284,500,000
6. 3,001,000,000
Write the number in standard form. 7. 3.41 106
8. 2.4 109
9. 5.0 101
10. Mathematicians Pythagoras, a Greek mathematician, was born about
2.6 103 years ago. Galileo, an Italian mathematician and astronomer, was born about 4.4 102 years ago. Who was born more recently?
Practice and Problem Solving with Example 1 2 3
Homework
Exercises 11–19, 36 20–28, 37 29–32
Online Resources
Write the number in scientific notation. 11. 41,200
12. 600
13. 29,200,000
14. 12,000,000
15. 154,000
16. 90,000,000,000
17. 102.4
18. 2000.1
19. 535
Write the number in standard form.
CLASSZONE.COM
• More Examples • eTutorial Plus
20. 7.1 10 5
21. 2 10 3
22. 8.29 10 4
23. 1.5 10 2
24. 3.52 10 5
25. 5.884 10 9
26. 3.5802 107
27. 6.07 101
28. 4.40044 10 6
Copy and complete the statement using , or . 29. 8.12 1015 _?_ 1.5 1017
30. 2.33 1010 _?_ 7.6 1010
31. 4.4 107 _?_ 44,000,000
32. 548,000,000 _?_ 5.48 107
Order the numbers from least to greatest. 33. 3.25 10 5 34. 7.8 10 3 35. 1.101 10 8
76
Chapter 2
Decimal Operations
3.5 10 5 8.7 10 4 1.1 10 8
7.98 10 4 8.02 10 3 1.01 10 9
2.61 106 7.18 10 4 1.11 10 8
1.10 107
Page 4 of 4
Monster Trucks In Exercises 36 and 37, use the following information. Bigfoot 5, the world’s largest monster truck, is 15 feet 5 inches tall and weighs 38,000 pounds. Each tire is 10 feet tall and weighs 2.4 103 pounds. 36. Write the weight of the truck in scientific notation. 37. Write the weight of one tire in standard form.
Find the missing number(s).
? 38. 46,000 4.6 10
39. 2. ? 6 10 6 ? ,560,000
40. Critical Thinking Multiply 3.6 104 by 1.4 106 by writing the
numbers in standard form, then multiplying. Express the product in scientific notation. Look at the exponents in the factors and in the product. What do you notice? 41. Challenge Find the sum of 9.18 10 4 and 4.8 10 5. Express your
answer in scientific notation. 42. Light-Years A light-year, the distance light travels in one year, is
5.88 1012 miles. The distance between Earth and the nearest star (other than the Sun) is 4.3 light-years. How many miles is this distance? Express your answer in standard form and in scientific notation.
Mixed Review Evaluate the expression when a 14 and b 7. (Lesson 1.2) 43. a b
44. 12 b 6
45. a 28 b
Find the quotient. Then check your answer. (Lesson 2.4) 46. 19.44 3.6
47. 1.372 0.28
48. 0.38 15.2
Basic Skills Find a low and high estimate for the product. 49.
62 31
50.
23 59
51.
52.
514 94
7398 617
Test-Taking Practice INTERNET
State Test Practice CLASSZONE.COM
53. Multiple Choice In 2001, the population of the United States was
about 278,000,000 people. Which choice expresses the population in scientific notation? A. 27.8 107
B. 2.78 10 8
C. 2.78 107
D. 278 10 6
54. Short Response Which is greater: 6.7263 107 or 68.763 106?
Explain your reasoning.
Lesson 2.5
Scientific Notation
77
Scientific Notation BEFORE
Now
WHY?
You multiplied whole numbers by powers of 10.
You’ll read and write numbers using scientific notation.
So you can compare the masses of Mars’s moons, as in Example 3.
In the Real World
Word Watch scientific notation, p. 74
Models Joseph King constructed a 23 foot model of the Eiffel Tower using 110,000 toothpicks. How can you use powers of 10 to write 110,000? One way to write large numbers is to use scientific notation.
Using Scientific Notation A number is written in scientific notation if it has the form c 10n where c is greater than or equal to 1 and less than 10 and n is a whole number. Standard form
Product form
Scientific notation
2,860,000
2.86 1,000,000
2.86 106
EXAMPLE
with
Vocabulary
Powers of ten: 101 10 102 100 103 1000 104 10,000 105 100,000 106 1,000,000
74
Chapter 2
1
Writing Numbers in Scientific Notation
As described above, Joseph King used 110,000 toothpicks to construct his Eiffel Tower model. To write 110,000 in scientific notation, use powers of 10. Standard form
Product form
Scientific notation
110,000
1.1 100,000
1.1 105
5 decimal places
5 zeros
Exponent is 5.
ANSWER Joseph King used 1.1 105 toothpicks to make his model of the Eiffel Tower.
Decimal Operations
Page 2 of 4
EXAMPLE
with
Reading
You read 7 103 as “seven times ten raised to the third power,” or “seven times ten cubed.”
2
Writing Numbers in Standard Form
Write the number in standard form. a. 7 103
b. 4.398 108
Solution Scientific notation a. 7 103 8
b. 4.398 10
Your turn now
Product form
Standard form
7 1000
7000
4.398 100,000,000
439,800,000
Write the number in scientific notation.
1. 450,000
2. 6,310,000
3. 10,000,000,000
Write the number in standard form. 4. 3.71 104
EXAMPLE
Astronomy
3
5. 9 107
6. 4.652 1010
Comparing Numbers in Scientific Notation
Mars Mars has two moons, Phobos and Deimos. Phobos has a mass of 1.06 1016 kilograms. Deimos has a mass of 2.4 1015 kilograms. Which moon has the greater mass? Solution To compare numbers written in scientific notation, first compare the exponents. If the exponents are equal, then compare the decimal parts. Phobos: 1.06 1016
Deimos: 2.4 1015
Because 16 > 15, 1.06 1016 > 2.4 1015. ■
Mars Mars is the fourth planet from the Sun. The distance between Mars and the Sun is about 1.416 108 miles. How can you write this distance in standard form?
ANSWER Phobos has a greater mass than Deimos.
✓Check
Write the numbers in standard form and compare.
1.06 1016 10,600,000,000,000,000 2.4 1015 2,400,000,000,000,000 So, 1.06 1016 > 2.4 1015.
Your turn now
Copy and complete the statement using < , >, or .
7. 9.74 1021 _?_ 2.1 1022
8. 5.28 1012 _?_ 5.3 1012
Lesson 2.5
Scientific Notation
75
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus CLASSZONE.COM
More Practice, p. 706
Getting Ready to Practice Vocabulary Tell whether the number is written in scientific notation, standard form, or neither. If neither, explain why. 1. 7.2 104
2. 34.2 105
3. 70,231
Write the number in scientific notation. 4. 75,000
5. 284,500,000
6. 3,001,000,000
Write the number in standard form. 7. 3.41 106
8. 2.4 109
9. 5.0 101
10. Mathematicians Pythagoras, a Greek mathematician, was born about
2.6 103 years ago. Galileo, an Italian mathematician and astronomer, was born about 4.4 102 years ago. Who was born more recently?
Practice and Problem Solving with Example 1 2 3
Homework
Exercises 11–19, 36 20–28, 37 29–32
Online Resources
Write the number in scientific notation. 11. 41,200
12. 600
13. 29,200,000
14. 12,000,000
15. 154,000
16. 90,000,000,000
17. 102.4
18. 2000.1
19. 535
Write the number in standard form.
CLASSZONE.COM
• More Examples • eTutorial Plus
20. 7.1 10 5
21. 2 10 3
22. 8.29 10 4
23. 1.5 10 2
24. 3.52 10 5
25. 5.884 10 9
26. 3.5802 107
27. 6.07 101
28. 4.40044 10 6
Copy and complete the statement using , or . 29. 8.12 1015 _?_ 1.5 1017
30. 2.33 1010 _?_ 7.6 1010
31. 4.4 107 _?_ 44,000,000
32. 548,000,000 _?_ 5.48 107
Order the numbers from least to greatest. 33. 3.25 10 5 34. 7.8 10 3 35. 1.101 10 8
76
Chapter 2
Decimal Operations
3.5 10 5 8.7 10 4 1.1 10 8
7.98 10 4 8.02 10 3 1.01 10 9
2.61 106 7.18 10 4 1.11 10 8
1.10 107
Page 4 of 4
Monster Trucks In Exercises 36 and 37, use the following information. Bigfoot 5, the world’s largest monster truck, is 15 feet 5 inches tall and weighs 38,000 pounds. Each tire is 10 feet tall and weighs 2.4 103 pounds. 36. Write the weight of the truck in scientific notation. 37. Write the weight of one tire in standard form.
Find the missing number(s).
? 38. 46,000 4.6 10
39. 2. ? 6 10 6 ? ,560,000
40. Critical Thinking Multiply 3.6 104 by 1.4 106 by writing the
numbers in standard form, then multiplying. Express the product in scientific notation. Look at the exponents in the factors and in the product. What do you notice? 41. Challenge Find the sum of 9.18 10 4 and 4.8 10 5. Express your
answer in scientific notation. 42. Light-Years A light-year, the distance light travels in one year, is
5.88 1012 miles. The distance between Earth and the nearest star (other than the Sun) is 4.3 light-years. How many miles is this distance? Express your answer in standard form and in scientific notation.
Mixed Review Evaluate the expression when a 14 and b 7. (Lesson 1.2) 43. a b
44. 12 b 6
45. a 28 b
Find the quotient. Then check your answer. (Lesson 2.4) 46. 19.44 3.6
47. 1.372 0.28
48. 0.38 15.2
Basic Skills Find a low and high estimate for the product. 49.
62 31
50.
23 59
51.
52.
514 94
7398 617
Test-Taking Practice INTERNET
State Test Practice CLASSZONE.COM
53. Multiple Choice In 2001, the population of the United States was
about 278,000,000 people. Which choice expresses the population in scientific notation? A. 27.8 107
B. 2.78 10 8
C. 2.78 107
D. 278 10 6
54. Short Response Which is greater: 6.7263 107 or 68.763 106?
Explain your reasoning.
Lesson 2.5
Scientific Notation
77
