10 CHAPTER 1 Critical Thinking Skills Estimation Techniques An important step in solving mathematical problems—or, in fact, any problem—is to make sure that the answer you’ve arrived at makes sense. One technique for determining whether an answer is reasonable is to estimate. Estimation is the process of arriving at an approximate answer to a question. This section demonstrates several estimation methods. To estimate, or approximate, an answer, we often round numbers, as illustrated in the following examples. The symbol ≈ means is approximately equal to. Example 1 Estimating the Cost of Chocolate Chip Cookies Malley decides to purchase chocolate chip cookies for a party. Estimate her cost if she purchases 21 cookies at $1.95 each. Solution We may round the amounts as follows to obtain an estimate. Number Number Rounded 21 $1.95 20 $2.00 $40.00 × × Thus, the 21 cookies would cost approximately $40.00, written $40.00. ≈ 7 Now try Exercise 25 In Example 1, the true cost is $1.95 21, × or $40.95. Estimates are not meant to give exact values for answers but are a means of determining whether your answer is reasonable. If you calculated an answer of $40.95 and then did a quick estimate to check it, you would know that the answer is reasonable because it is close to your estimated answer. Example 2 Two Ways to Estimate At a local discount retail store, Raj purchased a rug for $15.89, toothpaste for $1.49, diapers for $19.77, shampoo for $4.93, dog food for $12.88, and candy for $0.81. The cashier said the total bill was $69.51. Use estimation to determine whether this amount is reasonable. Solution The most expensive item is $19.77 and the least expensive is $0.81. How should we estimate? We will estimate two different ways. First, we will round the cost of each item to the nearest 10 cents. For the second method, we will round the cost of each item to the nearest dollar. Rounding to the nearest 10 cents is more accurate. To determine whether the total bill is reasonable, however, we may need to round only to the nearest dollar. Round to the Nearest 10 Cents Round to the Nearest Dollar Rug $15.89 → $15.90 $15.89 → $16.00 Toothpaste 1.49 → 1.50 1.49 → 1.00 Diapers 19.77 → 19.80 19.77 → 20.00 Shampoo 4.93 → 4.90 4.93 → 5.00 Dog food 12.88 → 12.90 12.88 → 13.00 Candy 0.81 → 0.80 0.81 → 1.00 $55.80 $56.00 Learning Catalytics Keyword: Angel-SOM-1.2 (See Preface for additional details.) Paul Maguire/Shutterstock
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