3-5

3-5 Multiplying Decimals

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpMultiply.

27,840

754,400

38,060

Course 1

3-5 Multiplying Decimals

120,700

14,112

62,760

1. 87 320

2. 943 800

3. 3,806 10

4. 1,207 100

5. 72 196

6. 120 523

Problem of the Day

Carmen and Rita sold homemade oatmeal cookies. After 8 days, they had sales totaling $70. Each day, their sales were $0.50 higher than the previous day. What were their sales on the first day?

$7.00

Course 1

3-5 Multiplying Decimals

Learn to multiply decimals by whole numbers and by decimals.

Course 1

3-5 Multiplying Decimals

Course 1

3-5 Multiplying Decimals

Additional Example 1: Science Application

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon?

Multiply 4 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.

17 4

68

Multiply as you would with whole numbers.

4 0.17

Course 1

3-5 Multiplying Decimals

Additional Example 1 Continued

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 4 lb dumbbell weigh on the Moon?

0.17 40.68

Place the decimal point by adding the number of decimal places in the numbers multiplied.

A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.

2 decimal places+ 0 decimal places

2 decimal places

Course 1

3-5 Multiplying Decimals

Check It Out: Example 1

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon?

Multiply 7 by 0.17, since 1 pound on Earth is 0.17 pound on the Moon.

17 7119

Multiply as you would with whole numbers.

7 0.17

Course 1

3-5 Multiplying Decimals

Check It Out: Example 1 Continued

Something that weighs 1 lb on Earth weighs 0.17 lb on the Moon. How much would a 7 lb dumbbell weigh on the Moon?

0.17 71.19

Place the decimal point by adding the number of decimal places in the numbers multiplied.

A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.

2 decimal places+ 0 decimal places

2 decimal places

Course 1

3-5 Multiplying Decimals

You can use a decimal grid to model multiplication of decimals.

Helpful Hint

Course 1

3-5 Multiplying Decimals

Additional Example 2A: Multiplying a Decimal by a Decimal

Find the product.

0.3 0.4

Multiply. Then place the decimal point.

0.3

0.4

1 decimal place

+ 1 decimal place

2 decimal places 0.12

Course 1

3-5 Multiplying Decimals

Additional Example 2B: Multiplying a Decimal by a Decimal

0.07 0.8

Multiply. Then place the decimal point.

0.07 0.8

2 decimal places + 1 decimal place3 decimal places; use a placeholder zero

0.056

Estimate the product. 0.8 is close to 1.

0.07 1 = 0.07

0.056 is close to the estimate of 0.07. The answer is reasonable.

Course 1

3-5 Multiplying Decimals

Additional Example 2C: Multiplying a Decimal by a Decimal

1.34 2.5

Multiply. Then place the decimal point.

1.34

2.52 decimal places

+ 1 decimal place

3 decimal places

670

Estimate the product. Round each factor to the nearest whole number.

1 3 = 3

3.350 is close to the estimate of 3. The answer is reasonable.

26803.350

Course 1

3-5 Multiplying Decimals

Check It Out: Example 2A

Find the product.

0.5 0.2

Multiply. Then place the decimal point.

0.5

0.21 decimal place

+ 1 decimal place

2 decimal places 0.10

Course 1

3-5 Multiplying Decimals

Check It Out: Example 2B

0.03 0.9

Multiply. Then place the decimal point.

0.03

0.92 decimal places

+ 1 decimal place3 decimal places; use a placeholder zero

0.027

Estimate the product. 0.9 is close to 1.

0.03 1 = 0.03

0.027 is close to the estimate of 0.03. The answer is reasonable.

Course 1

3-5 Multiplying Decimals

Check It Out: Example 2C

3.80 3.3

Multiply. Then place the decimal point.

3.80

3.32 decimal places

+ 1 decimal places

3 decimal places

1140

Estimate the product. Round each factor to the nearest whole number.

4 3 = 12

12.54 is close to the estimate of 12. The answer is reasonable.

1140012.540

Course 1

3-5 Multiplying Decimals

Additional Example 3A: Evaluating Decimal Expressions

Evaluate 5x for the value of x.

x = 3.062

3.062

53 decimal places

+ 0 decimal places

3 decimal places15.310

Substitute 3.062 for x. 5x = 5(3.062)

These notations all mean multiply 3 times x.

3 • x 3x 3(x)

Remember!

Course 1

3-5 Multiplying Decimals

Additional Example 3B: Evaluating Decimal Expressions

Evaluate 5x for the value of x.

x = 4.79

4.79

52 decimal places

+ 0 decimal places

2 decimal places 23.95

Substitute 4.79 for x. 5x = 5(4.79)

Course 1

3-5 Multiplying Decimals

Check It Out: Example 3A

Evaluate 5x for the value of x.

x = 2.012

2.012

53 decimal places

+ 0 decimal places

3 decimal places 10.060

Substitute 2.012 for x. 5x = 5(2.012)

Course 1

3-5 Multiplying Decimals

Check It Out: Example 3B

Evaluate 5x for the value of x.

x = 6.22

6.22

52 decimal places

+ 0 decimal places

2 decimal places 31.10

Substitute 6.22 for x. 5x = 5(6.22)

Lesson QuizFind each product.

1. 0.8

2. 0.006 0.07

Evaluate 8x for each value of x.

0.000420.056

Insert Lesson Title Here

21.64 6.432

Course 1

3-5 Multiplying Decimals

0.07

$87.40

3. x = 2.705 4. x = 0.804

5. “Pick your own” peaches sell for $0.95 per pound. You picked 92 pounds of peaches. How much were you charged?