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  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  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  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  1 decimal place + 1 decimal place2 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  decimal places + 1 decimal place3 decimal places; use a placeholder zero Estimate the product. 0.8 is close to  1 = is close to the estimate of 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  2 decimal places + 1 decimal place3 decimal places 670 Estimate the product. Round each factor to the nearest whole number. 1  3 = is close to the estimate of 3. The answer is reasonable

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

3-4 Multiplying Decimals Check It Out: Example 2B 0.03  0.9 Multiply. Then place the decimal point  2 decimal places + 1 decimal place3 decimal places; use a placeholder zero Estimate the product. 0.9 is close to  1 = is close to the estimate of The answer is reasonable.

3-4 Multiplying Decimals Check It Out: Example 2C 3.80  3.3 Multiply. Then place the decimal point  2 decimal places + 1 decimal places3 decimal places 1140 Estimate the product. Round each factor to the nearest whole number. 4  3 = is close to the estimate of 12. The answer is reasonable

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

3-4 Multiplying Decimals Additional Example 3B: Evaluating Decimal Expressions Evaluate 5x for the value of x. x =  2 decimal places + 0 decimal places2 decimal places 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 =  3 decimal places + 0 decimal places3 decimal places Substitute for x. 5x = 5(2.012)

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