3 4 Multiplying Decimals Learn to multiply decimals

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3 -4 Multiplying Decimals Learn to multiply decimals by whole numbers and by decimals.

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

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? 4 0. 17 17 4 68 Multiply 4 by 0. 17, since 1 pound on Earth is 0. 17 pound on the Moon. Multiply as you would with whole numbers.

3 -4 Multiplying Decimals Additional Example 1 Continued Something that weighs 1 lb on

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? Place the decimal point by adding the number of decimal places in the numbers multiplied. 0. 17 4 0. 68 2 decimal places + 0 decimal places 2 decimal places A 4 lb dumbbell on Earth weighs 0. 68 lb on the Moon.

3 -4 Multiplying Decimals Check It Out: Example 1 Something that weighs 1 lb

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? 7 0. 17 17 7 119 Multiply 7 by 0. 17, since 1 pound on Earth is 0. 17 pound on the Moon. Multiply as you would with whole numbers.

3 -4 Multiplying Decimals Check It Out: Example 1 Continued Something that weighs 1

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? Place the decimal point by adding the number of decimal places in the numbers multiplied. 0. 17 7 1. 19 2 decimal places + 0 decimal places 2 decimal places A 7 lb dumbbell on Earth weighs 1. 19 lb on the Moon.

3 -4 Multiplying Decimals Helpful Hint You can use a decimal grid to model

3 -4 Multiplying Decimals Helpful Hint You can use a decimal grid to model multiplication of decimals.

3 -4 Multiplying Decimals Additional Example 2 A: Multiplying a Decimal by a Decimal

3 -4 Multiplying Decimals Additional Example 2 A: Multiplying a Decimal by a Decimal Find the product. 0. 3 0. 4 Multiply. Then place the decimal point. 0. 3 1 decimal place 0. 4 + 1 decimal place 0. 12 2 decimal places

3 -4 Multiplying Decimals Additional Example 2 B: Multiplying a Decimal by a Decimal

3 -4 Multiplying Decimals Additional Example 2 B: Multiplying a Decimal by a Decimal 0. 07 0. 8 0. 07 1 = 0. 07 Estimate the product. 0. 8 is close to 1. 0. 07 0. 8 0. 056 Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places; use a placeholder zero 0. 056 is close to the estimate of 0. 07. The answer is reasonable.

3 -4 Multiplying Decimals Additional Example 2 C: Multiplying a Decimal by a Decimal

3 -4 Multiplying Decimals Additional Example 2 C: Multiplying a Decimal by a Decimal 1. 34 2. 5 1 3=3 1. 34 2. 5 670 2680 3. 350 Estimate the product. Round each factor to the nearest whole number. Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places 3. 350 is close to the estimate of 3. The answer is reasonable.

3 -4 Multiplying Decimals Check It Out: Example 2 A Find the product. 0.

3 -4 Multiplying Decimals Check It Out: Example 2 A Find the product. 0. 5 0. 2 Multiply. Then place the decimal point. 0. 5 1 decimal place 0. 2 + 1 decimal place 0. 10 2 decimal places

3 -4 Multiplying Decimals Check It Out: Example 2 B 0. 03 0. 9

3 -4 Multiplying Decimals Check It Out: Example 2 B 0. 03 0. 9 0. 03 1 = 0. 03 Estimate the product. 0. 9 is close to 1. 0. 03 0. 9 0. 027 Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places; use a placeholder zero 0. 027 is close to the estimate of 0. 03. The answer is reasonable.

3 -4 Multiplying Decimals Check It Out: Example 2 C 3. 80 3. 3

3 -4 Multiplying Decimals Check It Out: Example 2 C 3. 80 3. 3 4 3 = 12 3. 80 3. 3 11400 12. 540 Estimate the product. Round each factor to the nearest whole number. Multiply. Then place the decimal point. 2 decimal places + 1 decimal places 3 decimal places 12. 54 is close to the estimate of 12. The answer is reasonable.

3 -4 Multiplying Decimals Additional Example 3 A: Evaluating Decimal Expressions Evaluate 5 x

3 -4 Multiplying Decimals Additional Example 3 A: Evaluating Decimal Expressions Evaluate 5 x for the value of x. x = 3. 062 5 x = 5(3. 062) Substitute 3. 062 for x. 3. 062 3 decimal places 5 + 0 decimal places 15. 310 3 decimal places Remember! These notations all mean multiply 3 times x. 3 • x 3 x 3(x)

3 -4 Multiplying Decimals Additional Example 3 B: Evaluating Decimal Expressions Evaluate 5 x

3 -4 Multiplying Decimals Additional Example 3 B: Evaluating Decimal Expressions Evaluate 5 x for the value of x. x = 4. 79 5 x = 5(4. 79) Substitute 4. 79 for x. 4. 79 2 decimal places 5 + 0 decimal places 23. 95 2 decimal places

3 -4 Multiplying Decimals Check It Out: Example 3 A Evaluate 5 x for

3 -4 Multiplying Decimals Check It Out: Example 3 A Evaluate 5 x for the value of x. x = 2. 012 5 x = 5(2. 012) Substitute 2. 012 for x. 2. 012 3 decimal places 5 + 0 decimal places 10. 060 3 decimal places

3 -4 Multiplying Decimals Check It Out: Example 3 B Evaluate 5 x for

3 -4 Multiplying Decimals Check It Out: Example 3 B Evaluate 5 x for the value of x. x = 6. 22 5 x = 5(6. 22) Substitute 6. 22 for x. 6. 22 2 decimal places 5 + 0 decimal places 31. 10 2 decimal places