powers of 10
TRANSCRIPT
2-2 Powers of Ten and Scientific Notation
Course 2
Warm Up
Problem of the Day
Lesson Presentation
Warm UpFind each value.
1. 92
3. 152
5. 103
81 144
225
Course 2
2-2 Powers of Ten and Scientific Notation
2. 122
4. 102 100
6. 1041,000 10,000
Problem of the Day
Each day, Lowell runs one more lap than he did the day before. After seven days he has run 77 laps. How many laps did he run on the first day?8
Course 2
2-2 Powers of Ten and Scientific Notation
Learn to express large numbers in scientific notation.
Course 2
2-2 Powers of Ten and Scientific Notation
Vocabulary
standard formscientific notation
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Course 2
2-2 Powers of Ten and Scientific Notation
Course 2
2-2 Powers of Ten and Scientific Notation
The distance from Venus to the Sun is over 100,000,000 kilometers. You can write this number as a power of ten by using a base of ten and an exponent.
10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108
Power of ten
Course 2
2-2 Powers of Ten and Scientific Notation
The table shows several powers of ten.
Power of 10 Meaning Value
101
10 · 10 · 10 · 10
10 · 10 · 10
10 · 10
10 10
100
1,000
10,000
102
103
104
Multiply 14 · 103.
Additional Example 1: Multiplying by Powers of Ten
Course 2
2-2 Powers of Ten and Scientific Notation
14 · 103 = 14 · (10 · 10 · 10)
= 14 · 1,000
= 14,000
Use 10 as a factor 3 times.Multiply.
Try This: Example 1
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Course 2
2-2 Powers of Ten and Scientific Notation
Multiply 12 · 102.
12 · 102 = 12 · (10 · 10)
= 12 · 100
= 1,200
Use 10 as a factor 2 times.Multiply.
Course 2
2-2 Powers of Ten and Scientific Notation
You can also find the product of a number and a power of ten simply by moving the decimal point of the number. For powers of ten with positive exponents, move the decimal point to the right.
Find each product.
Additional Example 2: Multiplying by Powers of Ten Mentally
Course 2
2-2 Powers of Ten and Scientific Notation
A. 212 · 104
212 · 104 = 212.0000
= 2,120,000
4 places
Move the decimal point4 places.(You will need to add 4 zeros.)B. 31.6 · 103
31.6 · 103 = 31.6003 places
Move the decimal point 3 places.
= 31,600 (You will need to add2 zeros.)
Try This: Example 2
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Course 2
2-2 Powers of Ten and Scientific Notation
Find each product.
A. 22.5 · 102
22.5 · 102 = 22.50
= 2,250
2 places
Move the decimal point2 places.(You will need to add 1 zero.)B. 39.5 · 103
39.5 · 103 = 39.5003 places
Move the decimal point 3 places.
= 39,500 (You will need to add2 zeros.)
Course 2
2-2 Powers of Ten and Scientific Notation
Numbers are usually written in standard form. For example, 17,900,000 is in standard form. Scientific notation is a kind of shorthand that can be used to write large numbers. Numbers expressed in scientific notation are written as the product of two factors. In scientific notation, 17,900,000 is written as
A number greater than or equal to 1 but less than 10
A power of 10
Course 2
2-2 Powers of Ten and Scientific Notation
In scientific notation, it is customary to use a multiplication cross () instead of a dot.
Writing Math
Write the number in scientific notation.
Additional Example 3A: Writing Numbers in Scientific Notation
Course 2
2-2 Powers of Ten and Scientific Notation
A. 4,340,000
4,340,000 = 4,340,000Move the decimal point to get a number that is greaterthan or equal to 1 and less than 10.
= 4.34 106The exponent is equal to the number of places the decimal point is moved.
6 places
Additional Example 3B: Writing Numbers in Scientific Notation
Course 2
2-2 Powers of Ten and Scientific Notation
Write the number in scientific notation.
B. 327,000,000
327,000,000 = 327,000,000Move the decimal point to get a number that is greaterthan or equal to 1 and less than 10.
= 3.27 108The exponent is equal to the number of places the decimal point is moved.
8 places
Try This: Example 3A
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Course 2
2-2 Powers of Ten and Scientific Notation
Write the number in scientific notation.
A. 8,421,000
8,421,000 = 8,421,000Move the decimal point to get a number that is greaterthan or equal to 1 and less than 10.
= 8.421 106The exponent is equal to the number of places the decimal point is moved.
6 places
Try This: Example 3B
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Course 2
2-2 Powers of Ten and Scientific Notation
Write the number in scientific notation.
B. 327,000
327,000 = 327,000Move the decimal point to get a number that is greaterthan or equal to 1 and less than 10.
= 3.27 105The exponent is equal to the number of places the decimal point is moved.
5 places
The population of China in the year 2000 was estimated to be about 1.262 109. Write this number in standard form.
Additional Example 4: Writing Numbers in Standard Form
Course 2
2-2 Powers of Ten and Scientific Notation
1.262 109 = 1.262000000Since the exponent is 9, move the decimalpoint 9 places to the right.
= 1,262,000,000
The population of China was about 1,262,000,000people.
Try This: Example 4
The distance from the Earth to the Sun is calculated to be 1.5 108 kilometers. Write this distance in standard form.
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Course 2
2-2 Powers of Ten and Scientific Notation
1.5 108 = 1.50000000 Since the exponent is8, move the decimalpoint 8 places to theright.
= 150,000,000
The distance from the Earth to the Sun is about 150,000,000 kilometers.
Lesson Quiz: Part 1
Multiply.
180,000
2,500
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11,000
3,742
Course 2
2-2 Powers of Ten and Scientific Notation
1. 25 102
2. 18 104
3. 110 102
4. 3.742 103
Find each product.
Lesson Quiz: Part 2
Write each number in scientific notation..
5. 7,400,000
6. 45,000
7. Earth is about 9.292 107 miles from the Sun.
Write this number in standard form.
4.5 104
7.4 106
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92,920,000
Course 2
2-2 Powers of Ten and Scientific Notation