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4.4

Multiplying Decimals and Circumference of a Circle

Martin-Gay, Basic Mathematics, 4e 22

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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.

Martin-Gay, Basic Mathematics, 4e 33

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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.

Martin-Gay, Basic Mathematics, 4e 44

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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).

Martin-Gay, Basic Mathematics, 4e 55

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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.

Martin-Gay, Basic Mathematics, 4ed 66

1. Multiply 45.9 X 0.42 2. Multiply 0.112 X 0.6

278.19 1836

Practice Problems

91842.0

9.45

Multiplying Decimals

P 275

1 decimal place

2 decimal places

1+2=3 decimal places

0672.06.0

112.0

3 decimal places

1 decimal place

3+1=4 decimal places

Martin-Gay, Basic Mathematics, 4ed 77

3. Multiply 0.0721 X 48

4608.3 2884

Practice Problems

576848

0721.0

Multiplying Decimals

P 276

4 decimal place

0 decimal places

4+0=4 decimal places

Martin-Gay, Basic Mathematics, 4e 88

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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.

Martin-Gay, Basic Mathematics, 4ed 99

1748.90

27234

Estimating When Multiplying Decimals

Practice Problem 4

SOLUTION

Multiply:

Exact

Estimate

903

30

24208

98.2

26.30

98.2

26.30

Since 90.1748 is close to our estimate of 90, it is a reasonable answer.

P 276

6052

Round to the ones

Martin-Gay, Basic Mathematics, 4e 1010

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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.

0.501005.0

0006.001.006.0

Martin-Gay, Basic Mathematics, 4e 1111

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Example

Multiply.

a. 58.1 × 0.01

b. 85,624 × 0.1

c. 24.106 ×100

= 0.581 Move the decimal point 2 places to the left

= 8562.4 Move the decimal point 1 place to the left.

= 2410.6 Move the decimal point 2 places to the right.

Martin-Gay, Basic Mathematics, 4e 1212

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Problems Answers

5.

6.

7.

P 277

Practice Problems

107.23

Multiplying by Powers of 10

107.23 237

100004.203 100004.203 4.20300

100015.1 1000150.1 1150

Martin-Gay, Basic Mathematics, 4e 1313

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Problems Answers

8.

9.

10.

P 277

Practice Problems

1.62.7

Multiplying by Powers of 10

1.62.7 762.0

01.9.1 01.9.001 019.0

001.7682 001.7682 682.7

Martin-Gay, Basic Mathematics, 4e 1414

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Finding the Circumference of a Circle

Definition Example

Circumference: The distance around a circle.

diameter

radius

Circumference 2 radius Circumference diameter

The two common approximations for 22

are 3.14 and .7

Martin-Gay, Basic Mathematics, 4e 1515

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Example

Find the circumference of the following circle.

Circumference =

9.1 yards

2 9.1

2 r

yards 148.57

Martin-Gay, Basic Mathematics, 4e 1616

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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.

Martin-Gay, Basic Mathematics, 4e 1717

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Finding the Circumference of a Circle

Practice Problem 12

SOLUTION

Find the circumference of a circle whose radius is 11 meters. Then use the approximations 3.14 for π to approximate this circumference. 11 meters

112 meters 08.69

P 278

Martin-Gay, Basic Mathematics, 4e 1818

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DONE