Page 1 of 4 Multiplying and Dividing Decimals BEFORE Now WHY? You multiplied and divided integers and fractions. You’ll multiply and divide decimals. So you can find how many balloons you can buy, as in Ex. 24. In the Real World Word Watch leading digit, p. 251 Rafting You travel downstream in a raft at a rate of about 4.3 miles per hour. How far will you travel in 2.5 hours? Multiplying Decimals Words Multiply decimals as you do whole numbers. Then place the decimal point. The number of decimal places in the product is the total number of decimal places in the factors. Numbers 2.25 2 places EXAMPLE 1 8.9 1 place 20.025 3 places Multiplying Decimals To find how far you travel in the problem above about rafting, substitute the given values into the distance formula. Distance rate p time, so distance 4.3 p 2.5. 4.3 2.5 215 86 10.75 1 decimal place 1 decimal place 2 decimal places ANSWER You will travel about 10.75 miles. A number’s leading digit is its leftmost nonzero digit. To check that a product is reasonable, round each factor to its leading digit and multiply. 4.3 p 2.5 Round factors to leading digit. Your turn now 1. 7.39 p 2.1 4 p 3 12 ✓ Multiply. Show that your answer is reasonable. 2. 19.62 p 5.07 Lesson 5.7 3. 1.13 p 0.04 4. 0.85 p (8) Multiplying and Dividing Decimals 251 Page 2 of 4 Dividing Decimals Words When you divide by a decimal, multiply both the divisor and the dividend by the power of ten that will make the divisor an integer. Then divide. 5.5 Numbers 2.751 5 .1 2 5 Multiply by 100. 2751 5 1 2 .5 EXAMPLE 2 Dividing Decimals To find the quotient 60.102 6.3, multiply the divisor and dividend by 10. Move the decimal points 1 place to the right. 6.36 0 .1 0 2 Move decimal points. 636 0 1 .0 2 Then divide. 9.54 0 1 .0 2 636 ✓Check To check that the quotient is reasonable, round the quotient and the divisor to the leading digit. Then multiply. The result should be close in value to the dividend. 9.54 p 6.3 EXAMPLE 3 Round. 10 p 6 60 ✓ Using Zeros as Placeholders To find some quotients, you may need to use zeros as placeholders. Placeholder in Dividend Placeholder in Quotient 6 1.2 0.0126 1.8 .0 1.26 Zero as placeholder 5 0 126 60 0 Your turn now 252 Chapter 5 0.007 180 .1 2 6 126 0 Zeros as placeholders Find the quotient. 5. 1.6 0.04 6. 0.632 0.79 8. 4.365 (4.5) 9. 0.3744 1.56 Rational Number Operations 1.80 .0 1 2 6 7. 13 (0.65) 10. 0.0108 2.7 Page 3 of 4 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 731 Getting Ready to Practice 1. Vocabulary Copy the division problem. Use the words quotient, dividend, and divisor to label each number. _?_ _?_ 0.8 .2 97 _?_ Multiply or divide. Show that your answer is reasonable. 2. 7.8 p 2.6 3. 3.75 p 0.4 4. 13.2 1.1 5. 0.5 1.25 6. Guided Problem Solving A mother rhinoceros weighs 3600 pounds. Her baby weighs 0.38 of her weight. How much does the baby weigh? Explain why your answer is reasonable. 1 Write a verbal model to describe the problem. 2 Substitute the given values and solve. 3 Check to see that your answer is reasonable. Practice and Problem Solving HE L P with Homework Example 1 2 3 Exercises 7–22, 23, 25 7–22, 24, 26 7–22 Online Resources Find the product or quotient. 7. 25 p 0.2 8. 2.4 p 0.3 9. 8.2 p 0.7 11. 4.8 1.2 12. 4.9 0.07 13. 5 (0.1) 15. 5.41 p 0.35 16. 0.57 0.38 17. 4.844 0.56 18. 2.687 p (9) 19. 37.41 4.3 20. 0.098 p 0.55 22. 1.11 0.925 21. 6.025 p 48.2 10. 13.65 p 1.1 14. 8 (3.2) CLASSZONE.COM • More Examples • eTutorial Plus 23. Find the Error Describe and correct the error 9.78 3.4 39 1 2 2934 332.52 in the solution. 24. Balloons You are buying balloons that cost $.89 per package to decorate for a school dance. You have $14.75 to spend. How many packages of balloons can you buy? 25. Look for a Pattern Copy and complete the table by multiplying each number in the leftmost column by the number at the top of each other column. Describe the pattern. 1 0.1 0.01 0.001 0.0001 87 87 8.7 ? ? ? 356 356 ? ? ? ? 1200 ? ? ? ? ? Lesson 5.7 Multiplying and Dividing Decimals 253 Page 4 of 4 26. Lava Flows A lava flow is a stream of molten rock that pours from an erupting vent. A lava flow travels 15.5 miles down a steep slope in 2.5 hours. Find the average rate at which the flow travels. Write your answer in miles per hour. Explain why your answer is reasonable. Algebra Solve the equation. a 27. 9 0.9 c 28. 0.16 4.5 29. 1.2x 0.321 30. 8.25y 3.3 Evaluate the expression. 31. 3.4 3 5.1 1.7 4.89 32. 6.2 p (18.77 6.27) 9.1 2 33. Writing Explain how 4.6 divided by 0.23 is related to 460 divided by 23. Are the quotients the same? Why? Kilauea Volcano, Hawaii 34. Postal Rates The table shows rates to mail a first class letter. How much does it cost to mail a first class letter that weighs 3.5 ounces? First ounce or fraction of ounce $.37 Each additional ounce or fraction $.23 35. Critical Thinking How many decimal places does 1.3 1 have? 1.3 2? 1.3 3? 1.3 7? Explain your reasoning. 36. Challenge One micron is equal to 0.001 millimeter. If a bacteria is 4 microns wide, how many times would you have to magnify it for the bacteria to appear 1 millimeter wide? Mixed Review Write the number in standard form. (Lesson 4.8) 37. 6.89 10 9 38. 1.3 10 12 39. 7.405 10 6 Order the numbers from least to greatest. (Lesson 5.5) 3 9 11 40. 2.32, , 2.5, 2 , 2, 10 4 5 9 5 3 41. , 0.46, , , 0.4 20 12 8 Basic Skills Find the quotient. 42. 55 6 43. 127 5 44. 307 29 45. 8607 42 Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 46. Multiple Choice The quotient 0.57 0.38 is _?_. A. an integer B. negative C. more than 1 D. positive 47. Short Response You have $75 to spend on party decorations that cost $4.89 per bag, including tax. Find how many bags you can buy. Estimate to check that your answer is reasonable. Show your work. 254 Chapter 5 Rational Number Operations