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Page 1 of 4 Decimal Estimation BEFORE Now WHY? You estimated sums and differences of whole numbers. You’ll estimate sums and differences of decimals. So you can estimate change you’ll receive, as in Exs. 18 and 19. In the Real World Word Watch front-end estimation, p. 131 Sports The table shows the number of people, in millions, who participated in five sports in a recent year. About how many people played soccer? About how many more females participated in bicycling than in golf? One way to estimate a sum or a difference is to use rounding. EXAMPLE 1 Sports Participation (millions) Activity Bicycling Golf Hiking Soccer Swimming Males 22.9 21.8 14.9 8.2 27.0 Females 20.6 5.7 12.3 4.9 31.3 Estimating Sums and Differences a. To estimate the answer to the first real-world question above, round each decimal to the nearest whole number. Then add. 8.2 4.9 8 5 13 Round 8.2 down to 8. Round 4.9 up to 5. ANSWER About 13 million people played soccer. b. To estimate the answer to the second real-world question above, round each decimal to the nearest whole number. Then subtract. 20.6 5.7 21 6 15 Round 20.6 up to 21. Round 5.7 up to 6. ANSWER About 15 million more females participated in bicycling than in golf. Your turn now Use the information provided at the top of the page. 1. Estimate the total number of people who participated in hiking. 2. Estimate how many more males participated in swimming than in golf. 130 Chapter 3 Decimal Addition and Subtraction Page 2 of 4 EXAMPLE 2 Predicting Results Shopping You buy a T-shirt that costs $9.21. You give the clerk $20.00. Estimate your change. Is this estimate high or low? $20.00 $9.21 $20 $9 $11 Round 9.21 down to 9. ANSWER Your change is about $11. This estimate is high because you subtracted too little by rounding $9.21 down to $9. Front-End Estimation You can also estimate sums using front-end estimation . You add the front-end digits to get a low estimate. Then you use the remaining digits to adjust the sum and get a closer estimate. EXAMPLE 3 Using Front-End Estimation Groceries You have $10 to buy bread, milk, and cereal. If you have enough money, you would like to buy popcorn. The prices of these items are shown. Do you have enough money to buy popcorn? Grocery Lis t bread $ 1.79 milk $2.18 cereal $3.34 popcorn $3.65 Solution Find the sum of all the prices, including the price of the popcorn. 1 Add the front-end digits: the dollars. 2 Estimate the sum of the remaining digits: the cents. $1.79 $2.18 $3.34 $3.65 $9 $1.79 $2.18 $1 $3.34 $3.65 $1 $2 3 Add your results. $9 $2 $11 ANSWER You do not have enough money to buy popcorn. Your turn now Use front-end estimation to estimate the sum. 3. 6.42 7.64 3.94 2.21 4. 8.59 1.37 2 6.12 5. How can you estimate the difference in Example 2 so that your answer is a low estimate? Lesson 3.5 Decimal Estimation 131 Page 3 of 4 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 710 Getting Ready to Practice 1. Vocabulary Identify the front-end digits of $1.12 and $5.86. Use rounding to estimate the sum or difference. 2. 2.6 8.9 3. 12.43 5.8 4. 15.5 14.7 5. Guided Problem Solving A table is 73.66 centimeters tall. An iguana cage on the table is 76.2 centimeters tall. Estimate to decide whether they will fit beneath a shelf that is 157.16 centimeters off the floor. 1 Draw a diagram of the situation. 2 Estimate the height of the table and the cage combined. 3 Compare the combined heights to the height of the shelf. Practice and Problem Solving Use rounding to estimate the sum or difference. 6. 9.7 8.4 9. 7.2 4.6 7. 8.3 3.8 8. 9.3 6.9 10. 10.64 7.49 11. 2.25 0.93 12. 12.81 1.92 13. 10.72 2.85 14. 15.99 3.4 15. 12.38 12.8 16. 20.2 10.31 17. 9.1 8.98 Critical Thinking Estimate the change you will receive and tell whether the estimate is high or low. Explain. 18. You buy several postcards totaling $3.82. You give the clerk $10.00. 19. You buy a bag of pretzels for $1.15. You give the cashier $5.00. with Example 1 2 3 Homework Exercises 6–17 18–19 20–25 Use front-end estimation to estimate the sum. 20. 4.79 5.16 8.08 21. 6.23 4.75 3.91 22. 4.5 8.92 9.21 23. 6.46 3.22 2.58 24. 5.55 7.19 4.49 25. 6.31 2.5 1.93 26. Find the Error Describe and correct the error in the estimate. Online Resources $4 .79 $ 1 $ 1 .22 $6 CLASSZONE.COM • More Examples • eTutorial Plus 132 Chapter 3 Decimal Addition and Subtraction $6 $1 $7 Page 4 of 4 Geography Extended Problem Solving The Seven Summits are the highest mountain peaks on each of the seven continents. The heights of the summits are shown in the table. Use the table in Exercises 27–29. 27. Order the heights of the mountains from least to greatest. Then find the median of the heights. 28. Estimate the mean of the heights. Is your estimate high or low? Explain. 29. Critical Thinking Which of your answers in Exercises 27 and 28 is more representative of the heights? Explain. 30. Challenge How can you use rounding to ■ Mountains Most climbers of Mount Everest will start from the Everest Base Camp, which is about 3.2 miles high. About how far do they climb from the base camp to the top? overestimate the sum of two numbers? the difference of two numbers? How can you use rounding to underestimate the sum of two numbers? the difference of two numbers? Explain and show examples. Mountain Height (miles) Mount Elbrus (Europe) Mount Kosciusko (Australia) Mount Aconcagua (South America) Mount Everest (Asia) Mount Kilimanjaro (Africa) Mount McKinley (North America) Vinson Massif (Antarctica) 3.5 1.38 4.33 5.50 3.7 3.85 3.04 Mixed Review Evaluate the expression when x 2 and y 3. (Lesson 1.5) 31. x 14 32. 9y 33. x y 34. y x p y Round the decimal as specified. (Lesson 3.4) 35. 17.8023 (nearest thousandth) 36. 4.79663 (nearest hundredth) Basic Skills Find the sum or difference. 37. $10.75 $1.25 38. $9.80 $4.20 39. $2.85 $1.35 Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 40. Extended Response You have $25 to buy prizes for a game. The table shows the prizes and their prices. Use rounding to estimate the total cost and decide if this estimate is high or low. Then use front-end estimation to find the total cost. Which method is better when you have a fixed amount of money to spend? Explain. Lesson 3.5 Prize yo-yo bear sunglasses magic tricks set of books Decimal Estimation Price $1.48 $9.46 $1.07 $5.91 $8.00 133