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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.
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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
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$1
$7
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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
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