Page 1 of 5 Multiplying Decimals BEFORE Now WHY? You multiplied decimals by whole numbers. You’ll multiply decimals by decimals. So you can find the distance traveled by a turtle, as in Ex. 30. In the Real World Word Watch Review Words factor, p. 16 Sloths The sloth is commonly referred to as the “slowest mammal on Earth.” Its top speed on the ground is about 0.2 mile per hour. What is the farthest a sloth might go in 0.6 hour? EXAMPLE 1 Using a Model to Multiply Decimals To find how far a sloth might go in the question above, use a model to find the product 0.2 0.6. 0.6 1 Draw a 10-by-10 square. The whole square represents 1. Each small square 0.2 represents 1 hundredth, or 0.01. Each row or column represents 1 tenth, or 0.1. 2 Shade a rectangle that is 0.2 by 0.6. The area is 12 hundredths, because 12 small squares are shaded. So, 0.2 0.6 0.12. ANSWER The farthest a sloth might go in 0.6 hour is 0.12 mile. Your turn now Draw a model to find the product. 1. 0.1 0.7 2. 0.3 0.8 3. 0.9 0.7 Multiplying Decimals Words Multiply decimals as you do whole numbers. Then place the decimal point. The number of decimal places is the total number of decimal places in the factors. Numbers 3.14 2 places 164 Chapter 4 Decimal Multiplication and Division 15.6 1 place 48.984 3 places Page 2 of 5 EXAMPLE with Solving When you estimate to check a decimal product, you can use compatible numbers or round each decimal to its leading digit. Another estimate in Example 2 would be 300 0.8 240. 2 Placing a Decimal Point in a Product Place the decimal point in the correct location. 252.64 0.842 212.72288 2 places 3 places 5 places The first factor has 2 decimal places. The second factor has 3 decimal places. Because 2 3 5, the answer has 5 decimal places. ANSWER 252.64 0.842 212.72288 ✓ Check Estimate: 252.64 0.842 ≈ 250 1 250. So, the product 212.72288 is reasonable. EXAMPLE 3 Multiplying Decimals Find the product. a. 5.08 2.1 b. 1.159 0.03 c. 7.215 4.8 Solution 5.08 2.1 508 1016 10.668 2 decimal places 1 decimal place b. 1.159 0.03 0.03477 3 decimal places 2 decimal places 5 decimal places c. 7.215 4.8 57720 28860 34.6320 3 decimal places 1 decimal place a. tch Out! Wa You may need to write zeros in the product as placeholders in order to place the decimal point correctly. 3 decimal places 4 decimal places Once you place the decimal point, drop the zero at the end of the final answer. You write the product as 34.632. Your turn now 4. 2.15 5.4 Multiply. Use estimation to check your answer. 5. 12.7 2.9 6. 6.289 0.2 Lesson 4.3 7. 0.86 0.04 Multiplying Decimals 165 Page 3 of 5 EXAMPLE 4 Finding the Area of a Rectangle American Flag One of the largest flags ever made is about 153.9 meters long and 68.6 meters wide. Find the area of the flag to the nearest hundred square meters. Solution A lw Write the formula for the area of a rectangle. (153.9)(68.6) Substitute 153.9 for l and 68.6 for w. 10,557.54 Multiply. ANSWER The area of the flag is about 10,600 square meters. ✓ Check Round 153.9 to 150 and 68.6 to 70. Because 150 70 10,500, the product 10,600 is reasonable. The American flag hanging from the Hoover Dam is known as Superflag. Your turn now Find the area of the rectangle or square. 8. A square with side length 3.2 meters 9. A rectangle with length 8.1 inches and width 3.25 inches INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 711 Getting Ready to Practice 1. Vocabulary The number of decimal places in a product is equal to the _?_ of the number of decimal places in the factors. Find the product. 2. 0.4 0.9 3. 1.6 0.5 4. 1.18 0.02 5. 3.74 4.2 Geometry Find the area of the rectangle or square. 6. 7. 2.75 ft 2.5 cm 6.3 ft 2.5 cm 166 Chapter 4 Decimal Multiplication and Division Page 4 of 5 Practice and Problem Solving with Example 1 2 3 4 Homework Exercises 8–10 11–14 15–26, 29, 30 27, 28 Online Resources CLASSZONE.COM • More Examples • eTutorial Plus Draw a 10-by-10 square to model the product. 8. 0.4 0.5 9. 0.3 0.9 10. 0.1 0.6 11. Find the Error Describe and correct the error made in the solution. 7.5 3.8 600 225 285.0 Copy the answer and place the decimal point in the correct location. 12. 0.17 0.6 0102 13. 16.36 3.7 60532 14. 4.7 6.1 2867 Multiply. Use estimation to check that the product is reasonable. 15. 0.3 0.6 16. 1.1 0.4 17. 3.72 0.8 18. 4.91 2.3 19. 3.052 4.7 20. 2.05 5.8 21. 3.25 4.6 22. 1.08 0.45 23. 1.126 0.08 24. 3.201 0.03 25. 9.817 8.6 26. 6.87 9.61 Geometry Find the area of the rectangle or square. 27. 28. 8.1 cm 1.7 ft 1.7 ft 10.36 cm 29. Hair Growth Sophia’s hair grows at a rate of about 0.5 inch per month. How much does Sophia’s hair grow in 4.5 months? 30. Animals A turtle is traveling at a speed of 4.015 meters per minute. How far does the turtle travel in 8.5 minutes? Round your answer to the nearest meter. Number Sense Copy and complete the statement with <, >, or . 31. 64.2 1.12 _?_ 64 32. 2.2 0.12 _?_ 2.64 33. 32.5 0.01 _?_ 3.25 34. 0.505 10.1 _?_ 5.1005 Estimation Check that the location of the decimal point in the product is reasonable. Correct the answer if necessary. 35. 4.2 0.9; 37.8 36. 32.06 11.94; 3.827964 37. 109.452 5.7; 623.8764 38. 48.005 17.3; 83,0486.5 Lesson 4.3 Multiplying Decimals 167 Page 5 of 5 Delis In Exercises 39 and 40, use the table. It shows the prices of several foods. You buy 0.75 pound of ham, 0.5 pound of cheese, and 1.25 pounds of turkey. Food Ham Cheese Turkey Price per pound $5.49 $4.79 $4.25 39. Find the price of each item and the total amount you pay for these items. Round your result to the nearest cent. 40. Decide Can you buy 2.5 pounds of turkey if you have only $10? 41. Writing Explain when you need to include a zero as a placeholder in a product. Give an example. Critical Thinking Choose the correct response and explain your choice. 42. When you multiply two decimals between 0 and 1, is the product less than or greater than both factors? 43. When you multiply a number greater than 1 by a number between 0 and 1, is the product less than or greater than the first number? 44. Challenge The simple interest you might earn at a bank is found by the formula I Prt, where I is the simple interest, P is the principal, r is the interest rate, and t is the time. What will the simple interest be when P $200, r 0.03, and t 3.25? Mixed Review Graph the points on the same coordinate grid. (Lesson 2.6) 45. (2, 1) 46. (1, 4) 47. (0, 8) 48. (3, 0) 49. Clothesline Length In 1999, a clothesline loaded with clothes set a record at 15.02 miles long. Write the length of the clothesline in words. (Lesson 3.1) Basic Skills Divide. 50. 37 9 8 51. 41 3 4 0 52. 132 0 8 53. 213 1 5 Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 54. Multiple Choice Find the product 4.769 2.8. A. 133,532 B. 13,353.2 C. 133.532 D. 13.3532 55. Short Response Oranges cost $3.29 per pound. You buy 1.8 pounds for yourself and 2.3 pounds for your friend. How much do you spend on oranges to the nearest cent? Explain how you solved the problem. 168 Chapter 4 Decimal Multiplication and Division