 # Multiplying Decimals Now

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Multiplying Decimals
BEFORE
Now
WHY?
You multiplied decimals by
whole numbers.
You’ll multiply decimals by
decimals.
So you can find the distance
traveled by a turtle, as in Ex. 30.
In the Real World
Word Watch
Review Words
factor, p. 16
Sloths The sloth is commonly referred
to as the “slowest mammal on Earth.”
Its top speed on the ground is about
0.2 mile per hour. What is the farthest
a sloth might go in 0.6 hour?
EXAMPLE
1
Using a Model to Multiply Decimals
To find how far a sloth might go in the question above, use a model to
find the product 0.2 0.6.
0.6
1 Draw a 10-by-10 square. The whole
square represents 1. Each small square 0.2
represents 1 hundredth, or 0.01. Each
row or column represents 1 tenth, or 0.1.
2 Shade a rectangle that is 0.2 by 0.6. The
area is 12 hundredths, because 12 small
squares are shaded. So, 0.2 0.6 0.12.
ANSWER The farthest a sloth might go in
0.6 hour is 0.12 mile.
Draw a model to find the product.
1. 0.1 0.7
2. 0.3 0.8
3. 0.9 0.7
Multiplying Decimals
Words Multiply decimals as you do whole numbers. Then place
the decimal point. The number of decimal places is the total
number of decimal places in the factors.
Numbers
3.14
2 places
164
Chapter 4
Decimal Multiplication and Division
15.6
1 place
48.984
3 places
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EXAMPLE
with
Solving
When you estimate to
check a decimal product,
you can use compatible
numbers or round each
digit. Another estimate
in Example 2 would be
300 0.8 240.
2
Placing a Decimal Point in a Product
Place the decimal point in the correct location.
252.64 0.842 212.72288
2 places
3 places
5 places
The first factor has 2 decimal places. The second factor has 3 decimal
places. Because 2 3 5, the answer has 5 decimal places.
✓ Check
Estimate: 252.64 0.842 ≈ 250 1 250.
So, the product 212.72288 is reasonable.
EXAMPLE
3
Multiplying Decimals
Find the product.
a. 5.08 2.1
b. 1.159 0.03
c. 7.215 4.8
Solution
5.08
2.1
508
1016
10.668
2 decimal places
1 decimal place
b.
1.159
0.03
0.03477
3 decimal places
2 decimal places
5 decimal places
c.
7.215
4.8
57720
28860
34.6320
3 decimal places
1 decimal place
a.
tch Out!
Wa
You may need
to write zeros in the
product as placeholders in
order to place the decimal
point correctly.
3 decimal places
4 decimal places
Once you place the decimal point, drop the zero at the end of the
final answer. You write the product as 34.632.
4. 2.15 5.4
5. 12.7 2.9
6. 6.289 0.2
Lesson 4.3
7. 0.86 0.04
Multiplying Decimals
165
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EXAMPLE
4
Finding the Area of a Rectangle
153.9 meters long and 68.6 meters wide. Find the area of the flag
to the nearest hundred square meters.
Solution
A lw
Write the formula for the area of a rectangle.
(153.9)(68.6)
Substitute 153.9 for l and 68.6 for w.
10,557.54
Multiply.
✓ Check
Round 153.9 to 150 and 68.6 to 70. Because 150 70 10,500,
the product 10,600 is reasonable.
The American flag hanging
from the Hoover Dam is
known as Superflag.
Find the area of the rectangle or square.
8. A square with side length 3.2 meters
9. A rectangle with length 8.1 inches and width 3.25 inches
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Exercises
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More Practice, p. 711
1. Vocabulary The number of decimal places in a product is equal to the
_?_ of the number of decimal places in the factors.
Find the product.
2. 0.4 0.9
3. 1.6 0.5
4. 1.18 0.02
5. 3.74 4.2
Geometry Find the area of the rectangle or square.
6.
7.
2.75 ft
2.5 cm
6.3 ft
2.5 cm
166
Chapter 4
Decimal Multiplication and Division
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Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
8–10
11–14
15–26, 29, 30
27, 28
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Draw a 10-by-10 square to model the product.
8. 0.4 0.5
9. 0.3 0.9
10. 0.1 0.6
11. Find the Error Describe and correct the
7.5
3.8
600
225
285.0
Copy the answer and place the
decimal point in the correct location.
12. 0.17 0.6 0102
13. 16.36 3.7 60532
14. 4.7 6.1 2867
Multiply. Use estimation to check that the product is reasonable.
15. 0.3 0.6
16. 1.1 0.4
17. 3.72 0.8
18. 4.91 2.3
19. 3.052 4.7
20. 2.05 5.8
21. 3.25 4.6
22. 1.08 0.45
23. 1.126 0.08
24. 3.201 0.03
25. 9.817 8.6
26. 6.87 9.61
Geometry Find the area of the rectangle or square.
27.
28.
8.1 cm
1.7 ft
1.7 ft
10.36 cm
29. Hair Growth Sophia’s hair grows at a rate of about 0.5 inch per month.
How much does Sophia’s hair grow in 4.5 months?
30. Animals A turtle is traveling at a speed of 4.015 meters per minute.
How far does the turtle travel in 8.5 minutes? Round your answer to the
nearest meter.
Number Sense Copy and complete the statement with <, >, or .
31. 64.2 1.12 _?_ 64
32. 2.2 0.12 _?_ 2.64
33. 32.5 0.01 _?_ 3.25
34. 0.505 10.1 _?_ 5.1005
Estimation Check that the location of the decimal point in the
product is reasonable. Correct the answer if necessary.
35. 4.2 0.9; 37.8
36. 32.06 11.94; 3.827964
37. 109.452 5.7; 623.8764
38. 48.005 17.3; 83,0486.5
Lesson 4.3
Multiplying Decimals
167
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Delis In Exercises 39 and 40, use the
table. It shows the prices of several foods.
You buy 0.75 pound of ham, 0.5 pound of
cheese, and 1.25 pounds of turkey.
Food
Ham
Cheese
Turkey
Price per pound
\$5.49
\$4.79
\$4.25
39. Find the price of each item and
the total amount you pay for these items. Round your result to
the nearest cent.
40. Decide Can you buy 2.5 pounds of turkey if you have only \$10?
41. Writing Explain when you need to include a zero as a placeholder in a
product. Give an example.
Critical Thinking Choose the correct response and explain your choice.
42. When you multiply two decimals between 0 and 1, is the product less
than or greater than both factors?
43. When you multiply a number greater than 1 by a number between 0
and 1, is the product less than or greater than the first number?
44. Challenge The simple interest you might earn at a bank is found by
the formula I Prt, where I is the simple interest, P is the principal, r is
the interest rate, and t is the time. What will the simple interest be
when P \$200, r 0.03, and t 3.25?
Mixed Review
Graph the points on the same coordinate grid. (Lesson 2.6)
45. (2, 1)
46. (1, 4)
47. (0, 8)
48. (3, 0)
49. Clothesline Length In 1999, a clothesline loaded with clothes set a
record at 15.02 miles long. Write the length of the clothesline in words.
(Lesson 3.1)
Basic Skills Divide.
50. 37
9
8
51. 41
3
4
0
52. 132
0
8
53. 213
1
5
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
54. Multiple Choice Find the product 4.769 2.8.
A. 133,532
B. 13,353.2
C. 133.532
D. 13.3532
55. Short Response Oranges cost \$3.29 per pound. You buy 1.8 pounds
for yourself and 2.3 pounds for your friend. How much do you spend
on oranges to the nearest cent? Explain how you solved the problem.
168
Chapter 4
Decimal Multiplication and Division
``` # Hillsborough County Public Schools Elementary Mathematics Parent Connection # Changing a Percent to a Fraction or a Decimal 6.1 OBJECTIVES 