3-4 Scientific Notation

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson Quizzes

3-4 Scientific Notation

Warm UpMultiply.

1. 724 102

2. 837 10

3. 632.9 100

72,4008,370

63,290

3-4 Scientific Notation

Problem of the Day

A rope ladder is hanging from the back of a yacht. At 10:00 A.M., the water reaches the third step on the ladder. If the water rises the height of 2 steps every 2 hours, at what step would the water level be at 5:00 P.M.? Explain.

the third, because the boat will rise with the water

3-4 Scientific Notation

Learn to write large numbers in scientific notation.

3-4 Scientific Notation

Vocabulary

scientific notation

3-4 Scientific Notation

Additional Example 1A: Multiplying by Powers of Ten

Find each product.

5,892 1,000

5,892.000 There are 3 zeros in 1,000.

= 5,892,000 Write 3 placeholder zeros.

To multiply, move the decimal 3 places right.

3-4 Scientific Notation

Additional Example 1B: Multiplying by Powers of Ten

Find each product.

47.75 10,000

47.7500 There are 4 zeros in 10,000.

= 477,500 Write 4 placeholder zeros.

To multiply, move the decimal 4 places right.

3-4 Scientific Notation

Check It Out: Example 1A

Find each product.

901 1,000

901.000 There are 3 zeros in 1,000.

= 901,000 Write 3 placeholder zeros.

To multiply, move the decimal 3 places right.

3-4 Scientific Notation

Check It Out: Example 1B

Find each product.

15.425 10,000

15.4250 There are 4 zeros in 10,000.

= 154,250 Write 4 placeholder zeros.

To multiply, move the decimal 4 places right.

3-4 Scientific Notation

A number written in scientific notation has two numbers that are multiplied.

4.123 105

The first part is a number that is greater than or equal to 1 and less than 10.

The second part is a power of 10.

Scientific notation is a shorthand method that can be used to write large numbers.

3-4 Scientific Notation

Additional Example 2: Writing Numbers in Standard Notation

Write 6,000,000 in scientific notation.

6,000,000

6,000,000 = 6 106

6,000,000 Move the decimal point 6 places left.

The power of 10 is 6.

3-4 Scientific Notation

Check It Out: Example 2

Write 4,325,000 in scientific notation.

4,325,000 = 4.325 106

4,325,000 Move the decimal point 6 places left.

The power of 10 is 6.

3-4 Scientific Notation

You can write a large number written in scientific notation in standard form. Look at the power of 10 and move the decimal point that number of places to the right.

3-4 Scientific Notation

Additional Example 3: Writing Numbers in Standard From

Write 6.2174 103 in standard form.

6.2174 103

The power of 10 is 3.

6.2174 103 = 6,217.4

6.2174

Move the decimal point 3 places right.

3-4 Scientific Notation

Check It Out: Example 3

Write 3.21975 103 in standard form.

3.21975 103

The power of 10 is 3.

3.21975 103 = 3,219.75

3.21975

Move the decimal point 3 places right.

3-4 Scientific Notation

Additional Example 4

Write the distance to the sun, 93,000,000 miles, in scientific notation.

93,000,000 Move the decimal point left to form a number that is greater than or equal to 1 and less than 10.

9.3 107

93,000,000 Multiply that number by a power of ten.

The power of 10 is 7, because the decimal point is moved 7 places left.

The distance to the sun is 9.3 107.

3-4 Scientific Notation

Check It Out: Example 4

Write the distance 132,500 in scientific notation.

132,500Move the decimal point left to form a number that is greater than or equal to 1 and less than 10.

1.325 105

132,500 Multiply that number by a power of ten.

The power of 10 is 5, because the decimal point is moved 5 places left.

The distance is 1.325 105.

3-4 Scientific Notation

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

3-4 Scientific Notation

Lesson Quiz

Write each number in scientific notation.

1. 6,300

2. 70,400,000

Write each number in standard form.

3. 7.241 104

4. 8.2137 107

5. A Wall Street report indicated that a fast-moving stock had sold 3,295,000 shares. Write this number in scientific notation.

72,410

82,137,000

6.3 103

7.04 107

3.295 106

3-4 Scientific Notation

1. Which of the following represents 9,400 in scientific notation?

A. 9.4 102

B. 9.4 103

C. 94 102

D. 94 103

Lesson Quiz for Student Response Systems

3-4 Scientific Notation

2. Which of the following represents 5,328,000 in scientific notation?

A. 5328 103

B. 532.8 103

C. 53.28 105

D. 5.328 106

Lesson Quiz for Student Response Systems

3-4 Scientific Notation

3. Which of the following represents 1.1132 105 in scientific notation?

A. 11,132,000

B. 1,113,200

C. 111,320

D. 11,132

Lesson Quiz for Student Response Systems

3-4 Scientific Notation

4. Which of the following represents 7.9132 106 in scientific notation?

A. 79,132

B. 791,320

C. 7,913,200

D. 79,132,000

Lesson Quiz for Student Response Systems

3-4 Scientific Notation

5. Jupiter is at a distance of 778,600,000 km from the sun. Identify this number in scientific notation.

A. 7.786 108

B. 7.786 107

C. 7.786 106

D. 7.786 105

Lesson Quiz for Student Response Systems