1. 3-4 Multiplying Decimals Learn to multiply decimals by whole numbers and by decimals.

2. 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. 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  4 0.68 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

4. 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  7 119 Multiply as you would with whole numbers. 7  0.17

5. 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  7 1.19 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

6. 3-4 Multiplying Decimals You can use a decimal grid to model multiplication of decimals. Helpful Hint

7. 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 place2 decimal places 0.12

8. 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.

9. 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 2.5  2 decimal places + 1 decimal place3 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. 2680 3.350

10. 3-4 Multiplying Decimals Check It Out: Example 2A Find the product. 0.5  0.2 Multiply. Then place the decimal point. 0.5 0.2  1 decimal place + 1 decimal place2 decimal places 0.10

11. 3-4 Multiplying Decimals Check It Out: Example 2B 0.03  0.9 Multiply. Then place the decimal point. 0.03 0.9  2 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.

12. 3-4 Multiplying Decimals Check It Out: Example 2C 3.80  3.3 Multiply. Then place the decimal point. 3.80 3.3  2 decimal places + 1 decimal places3 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. 11400 12.540

13. 3-4 Multiplying Decimals Additional Example 3A: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 3.062 3.062 5  3 decimal places + 0 decimal places3 decimal places 15.310 Substitute 3.062 for x. 5x = 5(3.062) These notations all mean multiply 3 times x. 3 x3x3(x) Remember!

14. 3-4 Multiplying Decimals Additional Example 3B: Evaluating Decimal Expressions Evaluate 5x for the value of x. x = 4.79 4.79 5  2 decimal places + 0 decimal places2 decimal places 23.95 Substitute 4.79 for x. 5x = 5(4.79)

15. 3-4 Multiplying Decimals Check It Out: Example 3A Evaluate 5x for the value of x. x = 2.012 2.012 5  3 decimal places + 0 decimal places3 decimal places 10.060 Substitute 2.012 for x. 5x = 5(2.012)

16. 3-4 Multiplying Decimals Check It Out: Example 3B Evaluate 5x for the value of x. x = 6.22 6.22 5  2 decimal places + 0 decimal places2 decimal places 31.10 Substitute 6.22 for x. 5x = 5(6.22)