2-2 Powers of Ten and Scientific Notation

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson 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