copyright © 2012 pearson education, inc. publishing as prentice hall. 4.3 multiplying decimals and...

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

4.3

Multiplying Decimals and Circumference of a Circle

22

© 2012 Pearson Prentice Hall. All rights reserved

Multiplying Decimals

Multiplying decimals is similar to whole numbers. The only difference is that we place a decimal point in the product.

Multiplying DecimalsStep 1: Multiply the decimals as though they are whole numbers.Step 2: The decimal point in the product is placed so that the number of decimal places in the product is equal to the sum of the number of decimal place in the factors.

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Multiplying Decimals

Step Example

Step 1: Multiply the decimals as though they are whole numbers.

Multiply:

Step 2: The decimal point in the product is placed so that number of decimal places in the product is equal to the sum of the number of decimal places in the factors.

063

9.0

7.0

63.0

9.0

7.0

Total of 2 decimal places.

Decimal placed at two decimal places.

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Example

Multiply: 15.9 × 0.62

15.9

0.62

318

9540

9.858

1 decimal place

2 decimal places

Insert the decimal point in the product so that there are 3 decimal places (1 + 2 = 3).

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Example

Multiply: 0.648 × 0.5

0.648

0.5

0.3240

3 decimal places

1 decimal place

Insert the decimal point in the product so that there are 4 decimal places.

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Estimating when Multiplying Decimals

We can estimate when multiplying decimals to check for reasonableness.

Example:

Exact 5.3

4.2

106

2120

22.26

Estimate 5

4

20

Since 22.26 is close to our estimate of 20, it is a reasonable answer.

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Multiply 32.3 1.9.

Estimating when Multiplying Decimals

ExactExact EstimateEstimate

32.31.9

290.7323.061.37

rounds to 32rounds to 2

64

This is a reasonable answer.

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Multiplying Decimals by Powers of 10

There are some patterns that occur when we multiply a number by a power of ten, such as 10, 100, 1000, 10,000, and so on.

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Multiplying by Powers of 10

Type Example

Multiplying Decimals by Powers of 10 such as 10, 100, 1000 . . .: Move the decimal point to the right the same number of places as there are zeros in the power of 10.

Multiplying Decimals by Powers of 10 such as .1, .01, .001 . . .:

Move the decimal point to the left the same number of places as there are decimal places in the power of 10.

.501005.0

0006.001.006.0

1010


Move the decimal point to the right the same number of places as there are zeros in the power of 10.

Multiply: 3.4305 100

Since there are two zeros in 100, move the decimal place two places to the right.

3.4305 100 = 343.053.4305 =


1111


76.543 10 = 765.43

76.543 100 = 7654.3

76.543 100,000 = 7,654,300

Decimal point moved 1 place to the right.

Decimal point moved 2 places to the right.

Decimal point moved 5 places to the right.

2 zeros

5 zeros

1 zero

The decimal point is moved the same number of places as The decimal point is moved the same number of places as there are zeros in the power of 10.there are zeros in the power of 10.The decimal point is moved the same number of places as The decimal point is moved the same number of places as there are zeros in the power of 10.there are zeros in the power of 10.


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Move the decimal point to the left the same number of places as there are decimal places in the power of 10.

Multiply: 8.57 x 0.01

Since there are two decimal places in 0.01, move the decimal place two places to the left.

8.57 x 0.01 = 0.0857

Notice that zeros had to be inserted..Notice that zeros had to be inserted..

008.57 =


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Example

Multiply.

a. 58.1 × 0.01 = 0.581 Move the decimal point 2 places to the left.

b. 85,624 × 0.1 = 8562.4 Move the decimal point 1 place to the left.

c. 24.106 ×100 = 2410.6 Move the decimal point 2 places to the right.

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The distance around a polygon is called its perimeter.

The distance around a circle is called the circumference.

This distance depends on the radius or the diameter of the circle.

The Circumference of a Circle

1515


r

d

Circumference = 2··radiusor

Circumference = ·diameterC = 2 r or C = d


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The symbol is the Greek letter pi, pronounced “pie.” It is a constant between 3 and 4. A decimal approximation for is 3.14.A fraction approximation foris .

227

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Find the circumference of a circle whose radius is 4 inches.

4 inches

C = 2r = 2·4 = 8inches8inches is the exact circumference of this circle.

If we replace If we replace with the approximation 3.14, with the approximation 3.14, CC = 8 = 8 8(3.14) = 25.12 inches. 8(3.14) = 25.12 inches.25.12 inches is the 25.12 inches is the approximate circumference of the circumference of the circle.circle.


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Example

Find the circumference of the following circle.

Circumference =

9.1 yards

2 9.1

2 r

yards 148.57

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Solving Problems by Multiplying Decimals

Jose Severos, an electrician for Central Power and Light, worked 40 hours last week. Calculate his pay before taxes for last week if his hourly wage is $13.88.

13.88

40

0

55520

555.20

Jose Severos’ pay before taxes for last week is $555.20.

copyright © 2012 pearson education, inc. publishing as prentice hall. 4.3 multiplying decimals and...

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