1. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 1.2 Estimation

2. Copyright 2013, 2010, 2007, Pearson, Education, Inc. What You Will Learn Estimation 1.2-2

3. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Estimation The process of arriving at an approximate answer to a question is called estimation. Estimates are not meant to give exact values for answers, but are a means of determining whether your answer is reasonable. We often round numbers to estimate, or approximate, an answer. The symbol ≈ means is approximately equal to. 1.2-3

4. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Estimating the Cost of Bagels Sandy Mendez decides to purchase bagels for her colleagues. Estimate her cost if she purchases 29 bagels at $1.99 each. 1.2-4

5. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 1: Estimating the Cost of Bagels Solution: Round the amounts to obtain an estimate NumberNumber Rounded 29 30  $1.99 $2.00 $60.00 The 29 bagels will cost approximately $60.00, written ≈ $60.00 1.2-5

6. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using Estimates in Calculations The Martellos traveled 1276 miles from their home in Springfield, Missouri, to Yellowstone National Park. a)If their trip took 19.6 hours of driving time, estimate the average speed in miles per hour, that their car traveled. 1.2-6

7. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using Estimates in Calculations Solution: To estimate the average miles per hour, divide the number of miles by the number of hours. NumbersRounded The car averaged about 65 mph. 1.2-7

8. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using Estimates in Calculations The Martellos traveled 1276 miles from their home in Springfield, Missouri, to Yellowstone National Park. b)If their car used 52 gallons of gasoline, estimate the average gas mileage of their car, in miles per gallon. 1.2-8

9. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using Estimates in Calculations Solution: To estimate the average gas mileage, divide the number of miles by the number of gallons. NumbersRounded Car averaged about 26 mpg. 1.2-9

10. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using Estimates in Calculations The Martellos traveled 1276 miles from their home in Springfield, Missouri, to Yellowstone National Park. c)If the cost of gasoline averaged $3.51 per gallon, estimate the total cost of the gasoline used. 1.2-10

11. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Using Estimates in Calculations Solution: To estimate the total cost of gasoline, multiply the price per gallon by the number of gallons. NumbersRounded 52  $3.5150  $3.50 = $175 The cost of gasoline is about $175 1.2-11

12. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 5: Estimates on a Map Using the Oregon Trail, estimate the distance from Independence, Missouri, to Fort Hall in the Oregon Territory. 1.2-12

13. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 5: Estimates on a Map 1.2-13

14. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Solution: a) Approximately ¾-in represents 250 mi Mark off ¾-in intervals, from Independence, Missouri, to Fort Hall in the Oregon Territory, there are about 4, thus the distance is 4  250 mi or about 1000 mi 1.2-14 Example 5: Estimates on a Map