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Multiplying Decimals and
Whole Numbers
BEFORE
Now
WHY?
You multiplied whole numbers
by whole numbers.
You’ll multiply decimals and
whole numbers.
So you can find the length of a
race, as in Example 2.
You can use base-ten pieces to multiply.
Word Watch
commutative property of
multiplication, p. 155
associative property of
multiplication, p. 155
With base-ten pieces, one hundredth is represented by
one tenth is represented by
0.1.
1 Model 1 0.04.
2
Model 2 0.04.
0.01, and
3
Model 3 0.04.
This is one row of
4 hundredths.
1 0.04 0.04
2 0.04 0.08
3 0.04 0.12
Use a model to find the product.
1. 3 0.02
2. 3 0.2
3. 4 0.03
4. 4 0.3
5. How do the number of decimal places in your answers to Exercises 1–4 compare
to the number of decimal places in the factors?
Multiplying with Decimals When you multiply a decimal and a
whole number, the number of decimal places in the product is the same
as the number of decimal places in the decimal factor.
EXAMPLE
with
Solving
You may want to think of
Example 1 in words.
7 times 6 thousandths is
42 thousandths. Then you
can see why a zero is
needed as a placeholder
in the product.
1
Multiplying Decimals by Whole Numbers
Find the product 7 0.006.
Because 0.006 has 3 decimal places, the answer will have 3 decimal places.
0.006
7
0.042
Your turn now
1. 3 0.005
Write a zero as a placeholder so that
the answer has 3 decimal places.
Find the product. Then write the product in words.
2. 4 0.024
Lesson 4.1
3. 1.2 7
4. 2.36 5
Multiplying Decimals and Whole Numbers
153
Page 2 of 5
Counting Zeros You need to include the zeros at the end of a
product in order to count the decimal places correctly. Once you place
the decimal point, however, you can drop any zeros that occur at the end
of the answer, as in Example 2 below.
Sports
EXAMPLE
2
Solving a Problem
Junior Iditarod Race In the 2001 Junior Iditarod race, one team
completed the race in about 18 hours over two days. The team’s
average rate was 8.875 miles per hour. About how long was the race?
Round to the nearest mile.
Solution
Use the formula Distance Rate Time.
8.875
18
71000
8875
159.750
■
Place the decimal point
before dropping any zeros.
Iditarod Race
Fourteen teams competed in
the 2001 Junior Iditarod race
in Alaska. The musher (or
driver) for each team of dogs
was between the ages of 14
and 17. If each team had
7–10 dogs, estimate how
many dogs participated in
the race.
ANSWER The race was about 160 miles long.
EXAMPLE
3
Checking for Reasonableness
Use estimation to check that the answer to Example 2 is reasonable.
Distance 8.875 18
≈ 9 18
Round 8.875 to its leading digit.
162
ANSWER Because 160 is close to 162, the distance is reasonable.
Your turn now
Find the product.
5. 0.9 50
6. 1.505 8
7. 3.14 75
8. 6.25 22
Use estimation to check that the answer is reasonable.
9. 3.254 18; 58.572
10. 12.706 3; 381.18
11. Explain why the answer 84 is not reasonable for the product 3 2.8.
12. Explain why the answer 1.06 is reasonable for the product 2 0.53.
154
Chapter 4
Decimal Multiplication and Division
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Properties of Multiplication You used properties of addition
in Lesson 3.6. Similar properties for multiplication are shown below.
Properties of Multiplication
Commutative Property In a product, you can multiply
numbers in any order.
Numbers 2 6.5 6.5 2
Algebra a p b b p a
Associative Property The value of a product does not
depend on how the numbers are grouped.
Numbers (2 6.5) 4 2 (6.5 4)
Algebra (a p b) p c a p (b p c)
EXAMPLE
4
Using Properties of Multiplication
Tell whether the commutative or associative property of multiplication
allows you to rewrite the problem as shown. Explain your choice.
a. 5 3.25 2 3.25 5 2
The order of the numbers has
changed, so this is an example
of the commutative property
of multiplication.
b. (3.25 5) 2 3.25 (5 2)
The numbers that are grouped
have changed, so this is an
example of the associative
property of multiplication.
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Exercises
eWorkbook Plus
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More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Which property does (2 p 8) p 9 2 p (8 p 9) illustrate?
Copy the answer and place the decimal point in the correct location.
2. 34 1.6 544
3. 15 1.04 1560
4. 7.841 3 23523
Find the product. Then write the product in words.
5. 3 0.2
6. 6 0.9
Lesson 4.1
7. 3.164 5
8. 2.78 45
Multiplying Decimals and Whole Numbers
155
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
9–27
12–27, 30–33
16–27, 34, 35
28, 29
Online Resources
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Use a model to find the product. Then write the product in words.
9. 4 0.2
10. 6 0.03
11. 2 0.03
Copy the answer and place the decimal point in the correct location.
12. 27 5.34 14418
13. 9 0.873 7857
15. Find the Error Describe and
14. 2.03 5 1015
0.0028
4
0 0.1 1 2
correct the error in the solution.
• More Examples
• eTutorial Plus
Find the product. Use estimation to check your answer.
16. 6 3.5
17. 9 2.17
18. 0.008 9
19. 5.31 18
20. 0.29 82
21. 0.32 55
22. 7.25 34
23. 3.072 8
24. 9.426 3
25. 2.125 15
26. 52 0.088
27. 18 0.005
Copy and complete each statement. Tell whether you used the
commutative or associative property of multiplication.
28. 2 79 0.5 79 _?_ 0.5
29. (0.4 83) 5 0.4 (_?_ 5)
Shopping Find the amount you would spend in the situation.
30. You want to buy balloons for a friend’s birthday. The balloons cost
$1.50 each. You buy 6 balloons.
31. Each ticket for a rock concert costs $48.35. You buy 7 tickets.
32. It costs $.12 to make a photocopy. You make 84 photocopies.
33. A paintbrush costs $3.79. You buy 11 of them.
Number Sense Use estimation to explain why the statement is false.
34. The product of 5 and 0.85 is more than 5.
35. The product of 24 and 1.107 is less than 24.
36. Bottled Water A beverage company packages spring water in bottles
that hold 1.5 liters. How many liters of water are in a case that contains
8 bottles? How many liters are in a case that contains 12 bottles?
37. Writing Explain why you can drop the zero at the end of the products
in your answers to Exercise 36. Why might you need to keep the final
zero in the product for a situation involving money?
156
Chapter 4
Decimal Multiplication and Division
Page 5 of 5
38. Armor The table at the right
shows the heights of three
suits of armor. Change the
heights from centimeters to
inches. Use the fact that
1 cm ≈ 0.3937 in.
Type of
Armor
Adult
Child
Dog
Height (cm)
185
109
64
Height (in.)
_?_
_?_
_?_
Algebra Evaluate the variable expression.
39. 120x 3, when x 0.1
40. 7 16x, when x 4.2
41. Challenge Use estimation to find a decimal that when multiplied by
18 gives a product between 24 and 30.
Mixed Review
Evaluate the expression. (Lesson 1.4)
42. 104 5 2 7
43. 5 (36 3)
44. 28 2 32
Use front-end estimation to estimate the sum. (Lesson 3.5)
45. 3.64 8.22 2.15
46. 7.1 2.83 2.15
Choose a Strategy Use a strategy from
the list to solve the following problem.
Explain your choice of strategy.
47. 1.7 6.1 3.28
Problem Solving Strategies
Draw a Diagram
Make a List
■ Make a Table
■ Look for a Pattern
■
■
48. You are at an awards dinner and have
a choice of 3 dinner entrees, 2 side
dishes, and 2 desserts. You can choose
only one of each. How many different
meals can you select?
Basic Skills Write the place value of the red digit.
49. 320,840
50. 340,875
51. 1,263,920
Test-Taking Practice
INTERNET
State Test Practice
52. Multiple Choice Tracy bought 39 basketball tickets that cost $19.25
each. What is the best estimate of the amount Tracy spent?
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A. $600
B. $700
C. $800
D. $900
53. Short Response Kari works five days per week and four hours per day.
If she earns $9.75 per hour, how much does she earn per week? Explain
how you found your answer.
Lesson 4.1
Multiplying Decimals and Whole Numbers
157