3-4 Multiplying Decimals

Warm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

3-4 Multiplying Decimals

Warm UpMultiply.

27,840

754,400

38,060120,700

14,112

62,760

1. 87 320

2. 943 800

3. 3,806 10

4. 1,207 100

5. 72 196

6. 120 523

3-4 Multiplying Decimals

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

3-4 Multiplying Decimals

Learn to multiply decimals by whole numbers and by decimals.

3-4 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

3-4 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

3-4 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

3-4 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

3-4 Multiplying Decimals

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

Helpful Hint

3-4 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

3-4 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.

3-4 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

3-4 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

3-4 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.

3-4 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

3-4 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!

3-4 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)

3-4 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)

3-4 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)

3-4 Multiplying Decimals

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

3-4 Multiplying Decimals

Lesson Quiz

Find each product.

1. 0.8 0.07

2. 0.006 0.07

Evaluate 8x for each value of x.

0.00042

0.056

21.64 6.432

$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?

3-4 Multiplying Decimals

1. Identify the product.

0.29 0.01

A. 0.29

B. 0.029

C. 0.0029

D. 0.00029

Lesson Quiz for Student Response Systems

3-4 Multiplying Decimals

2. Identify the product.

0.052 0.03

A. 1.0056

B. 0.1056

C. 0.0156

D. 0.00156

Lesson Quiz for Student Response Systems

3-4 Multiplying Decimals

3. Evaluate 4x for x = 5.325.

A. 21

B. 21.2

C. 21.28

D. 21.3

Lesson Quiz for Student Response Systems

3-4 Multiplying Decimals

4. Evaluate 9x for x = 0.012.

A. 10.8

B. 1.08

C. 0.108

D. 0.0108

Lesson Quiz for Student Response Systems

3-4 Multiplying Decimals

5. Strawberry lemonade costs $0.89 per packet. Karen bought 58 packets of strawberry lemonade for a picnic. How much did she pay for it?

A. $51.62

B. $51.86

C. $52.54

D. $52.93

Lesson Quiz for Student Response Systems