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Learn to multiply decimals by whole numbers and by decimals.

Learn to multiply decimals by whole numbers and by 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.

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Learn to multiply decimals by whole numbers and by decimals.

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  1. Learn to multiply decimals by whole numbers and by decimals.

  2. 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. 4  0.17 17 Multiply as you would with whole numbers.  4 68

  3. 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 2 decimal places  4 + 0 decimal places 0.68 2 decimal places A 4 lb dumbbell on Earth weighs 0.68 lb on the Moon.

  4. 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. 7  0.17 17 Multiply as you would with whole numbers.  7 119

  5. 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 2 decimal places  7 + 0 decimal places 1.19 2 decimal places A 7 lb dumbbell on Earth weighs 1.19 lb on the Moon.

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

  7. Multiply. Then place the decimal point. 1 decimal place + 1 decimal place 2 decimal places Additional Example 2A: Multiplying a Decimal by a Decimal Find the product. 0.3  0.4 0.3  0.4 0.12

  8. Estimate the product. 0.8 is close to 1. Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places; use a placeholder zero Additional Example 2B: Multiplying a Decimal by a Decimal 0.07  0.8 0.07  1 = 0.07 0.07 0.8 0.056 0.056 is close to the estimate of 0.07. The answer is reasonable.

  9. 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 Additional Example 2C: Multiplying a Decimal by a Decimal 1.34  2.5 1  3 = 3 1.34  2.5 670 2680 3.350 3.350 is close to the estimate of 3. The answer is reasonable.

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

  11. Estimate the product. 0.9 is close to 1. Multiply. Then place the decimal point. 2 decimal places + 1 decimal place 3 decimal places; use a placeholder zero Check It Out: Example 2B 0.03  0.9 0.03  1 = 0.03 0.03  0.9 0.027 0.027 is close to the estimate of 0.03. The answer is reasonable.

  12. 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 Check It Out: Example 2C 3.80  3.3 4  3 = 12 3.80  3.3 1140 11400 12.540 12.54 is close to the estimate of 12. The answer is reasonable.

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

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

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

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

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