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3-5 Scientific Notation

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Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpMultiply.

1. 724 102

2. 837 10

3. 632.9 100

4. 18,256 10

5. 10 10 10

72,400

8,370

63,290

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182,560

1,000

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 every 2 hours the water rises the height of two steps, at what step would the water level be at 5:00 P.M.? Explain.

the third, because the boat will rise with the water

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Learn to write large numbers in scientific notation.

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Vocabulary

scientific notation

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Scientific notation is a shorthand method for writing large numbers like 3,456,000.

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To write the number 3,456,000 in scientific notation, do the following:

3,456,000Move the decimal point left to form a number that is greater than 1 and less than 10.

3,456,000 Multiply that number by a power of ten.

3.456 106The power of 10 is 6, because the decimal point is moved 6 places left.

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The number of zeros in the power of ten, or the exponents in the power of ten, tells you how many places to move the decimal point

Remember!

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

3.456 106

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

The second part is a power of 10.

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Additional Example 1A & 1B: Writing Numbers in Scientific Notation

Write each number in scientific notation.

A. 6,000,000

B. 411,000

6,000,000 Move the decimal point 6 places left. The power of 10 is 6.

6,000,000 = 6 106

411,000 Move the decimal point 5 places left. The power of 10 is 5.

411,000 = 4.11 105

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Additional Example 1C: Writing Numbers in Scientific Notation

Write the number in scientific notation.

C. 79,000,000


79,000,000 = 7.9 107

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Try This: Example 1A & 1B


A. 8,000,000

B. 587,000


8,000,000 = 8 106

587,000 Move the decimal point 5 places left. The power of 10 is 5.

587,000 = 5.87 105

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Try This: Example 1C

Write the number in scientific notation.

C. 13,000,000


13,000,000 = 1.3 107

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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.

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Additional Example 2A & 2B: Writing Numbers in Standard From

Write each number in standard form.

A. 6.2174 103

B. 9.5 108

The power of 10 is 3.

6.2174 103 = 6,217.4

6.2174


9.50000000

Move the decimal point 3 places right.

Move the decimal point 8 places right. Use zeros as placeholders. 9.5 108 = 950,000,000

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Additional Example 2C: Writing Numbers in Standard From

Write the number in standard form.

C. 4.83 105 The power of 10 is 5.

4.83 105 = 483,000

4.83000 Move the decimal point 5 places right. Use zeros as placeholders.

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Try This: Example 2A & 2B


A. 8.1974 103

B. 2.3 106


8.1974 103 = 8,197.4

8.1974

The power of 10 is 6. 2.300000

Move the decimal point 3 places right.

Move the decimal point 6 places right. Use zeros as placeholders. 2.3 106 = 2,300,000

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Try This: Example 2C

Write the number in standard form.

C. 9.77 105 The power of 10 is 5.

9.77 105 = 977,000

9.77000Move the decimal point 5 places right. Use zeros as placeholders.

Lesson Quiz


1. 6,300

2. 70,400,000


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.

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72,410

82,137,000

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6.3 103

7.04 107

3.295 106

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