3 4 Multiplying Decimals To multiply decimals multiply

3 -4 Multiplying Decimals To multiply decimals, multiply as you would with integers. To place the decimal point in the product, count the number of decimal places in each factor. The product should have the same number of decimal places in the factors. 7 8 56 0. 7 0. 8 0. 56 Same digits 1 decimal place + 1 decimal place 2 decimal places

3 -4 Multiplying Decimals Additional Example 1: Multiplying Integers by Decimals Multiply. A. 7 · 0. 1 7 0. 1 0. 7 0 decimal places 1 decimal place 0 + 1 = 1 decimal place B. – 3 · 0. 03 – 3 0. 03 – 0. 09 0 decimal places 2 decimal places 0 + 2 = 2 decimal places. Use zero as a place holder.

3 -4 Multiplying Decimals Additional Example 1: Multiplying Integers by Decimals Multiply. C. 2. 45 · 35 2. 45 35 12 25 + 73 50 85. 75 2 decimal places 0 decimal places 2 + 0 = 2 decimal places

3 -4 Multiplying Decimals Check It Out: Example 1 Multiply. A. 3 · 1. 2 3 1. 2 6 + 30 3. 6 B. – 5 · 0. 05 – 5 0. 02 – 0. 25

3 -4 Multiplying Decimals Check It Out: Example 1 Multiply. C. 6. 04 · 11 6. 04 11 604 + 6040 66. 44

3 -4 Multiplying Decimals Additional Example 2 A: Multiplying Decimals by Decimals Multiply. Estimate to check whether each answer is reasonable. – 3. 84 · 0. 9 – 3. 84 0. 9 – 3. 456 Estimate – 4 · 1 = – 4 2 decimal places 1 decimal place 2 + 1 = 3 decimal places – 3. 456 is a reasonable answer.

3 -4 Multiplying Decimals Additional Example 2 B: Multiplying Decimals by Decimals Simplify. Estimate to check whether each answer is reasonable. (2. 9)² (2. 9) 2. 9 261 + 580 8. 41 2. 9 is a factor 2 times 1 decimal place 1 + 1 = 2 decimal places Estimate (2. 9)² = 3 · 3 = 9 8. 41 is a reasonable answer.

3 -4 Multiplying Decimals Check It Out: Example 2 A Simplify. Estimate to check whether each answer is reasonable. – 0. 05 0. 5 – 0. 025

3 -4 Multiplying Decimals Check It Out: Example 2 B Simplify. Estimate to check whether each answer is reasonable. 1. 36 0. 22 272 + 2720 0. 2992

3 -4 Multiplying Decimals Check It Out: Example 2 C Simplify. Estimate to check whether each answer is reasonable. (-0. 6)3 (– 0. 6) – 0. 6 0. 36 – 0. 6 – 0. 216

3 -4 Multiplying Decimals Check It Out: Example 2 D Simplify. Estimate to check whether each answer is reasonable. (4. 2) 2 (4. 2) 4. 2 84 +1680 17. 64

3 -4 Multiplying Decimals Additional Example 3: Application To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is 0. 38. What would a person who weighs 85 pounds on Earth weigh on Mars? 0. 38 85 1 90 + 30 40 32. 30 2 decimal places 0 decimal places 2 + 0 = 2 decimal places

3 -4 Multiplying Decimals Additional Example 3 Continued To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is 0. 38. What would a person who weighs 85 pounds on Earth weigh on Mars? Estimate 0. 5 • 80 = 40 32. 30 is a reasonable answer. The person would weigh 32. 30 pounds on Mars.

3 -4 Multiplying Decimals Check It Out: Example 3 A On average, people ages 13 to 15 years old sleep 9. 5 hours a day. How many hours does the average teenager spend sleeping in a year? 365 9. 5 1825 + 32850 3467. 5 hours

3 -4 Multiplying Decimals Check It Out: Example 3 B Maria commutes to and from work on the train 20 days each month. Her train ride each way lasts 1. 2 hours. How many hours does she spend commuting to work each month? 20 days × 2 rides per day = 40 rides per month 1. 2 40 48. 0 hours

3 -4 Multiplying Decimals Lesson Quiz Multiply. 1. 9 · 0. 7 2. (1. 5)2 6. 3 2. 25 Multiply. Estimate to check whether each answer is reasonable. 3. 3. 4 · 4. 1 13. 94; Estimate: 3 • 4 = 12 4. 7. 62 · (– 5. 4) – 41. 148; Estimate: 8 • (– 5) = – 40 5. Dennis runs 7. 2 miles per day. How far does he run in 5 days? 36 miles