Download Multiplying and Dividing by Powers of Ten

Page 1 of 4
Multiplying and Dividing by
Powers of Ten
BEFORE
Now
WHY?
You multiplied and divided with
decimals.
You’ll use mental math to help
multiply and divide.
So you can find the number of
hockey players in Exs. 36–37.
What happens when you multiply by a power of ten?
Word Watch
1 Complete the table.
Review Words
power, p. 16
exponent, p. 16
2 What do you notice about
the movement of the decimal
point when you multiply by
whole number powers of 10?
by decimal powers of 10?
Whole Number
Powers of Ten
10 8.3 _?_
100 8.3 _?_
1000 8.3 _?_
10,000 8.3 _?_
Decimal
Powers of Ten
0.1 8.3 _?_
0.01 8.3 _?_
0.001 8.3 _?_
0.0001 8.3 _?_
Multiplying by Powers of Ten
Multiplying by Whole Number Powers of 10 Move the
decimal point one place to the right for each zero in the
whole number power of 10.
Numbers 3.995 100 3 9 9 . 5
Multiplying by Decimal Powers of 10 Move the decimal
point one place to the left for each decimal place in the
decimal power of 10.
Numbers 399.5 0.001 0 . 3 9 9 5
EXAMPLE
1
Multiply Decimals Using Mental Math
a. 0.05 1000 0 0 5 0. 50
with
Solving
b. 95.38 0.0001 .0 0 9 5 3 8 0.009538
When you move a decimal
point to the right or left,
you may need to write
zeros as placeholders.
Your turn now
Chapter 4
Move 4 places to the left.
Find the product using mental math.
1. 21.48 10
176
Move 3 places to the right.
Decimal Multiplication and Division
2. 6.07 1000
3. 153.6 0.01
4. 12 0.001
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EXAMPLE
2
Multiply Decimals by Powers of Ten
Bridges The graph shows the number of vehicles that crossed bridges
during 2000. How many vehicles crossed the Golden Gate Bridge?
Vehicle Traffic in 2000
Francis Scott Key Bridge (MD)
Golden Gate Bridge (CA)
George Washington Bridge (NY)
1.09
4.25
5.34
10,000,000 vehicles
4.25 10,000,000 4 2 5 0 0 0 0 0.
Move 7 places to the right.
42,500,000
ANSWER In 2000, 42,500,000 vehicles crossed the Golden Gate Bridge.
Dividing by Powers of Ten
Dividing by Whole Number Powers of 10 Move the
decimal point one place to the left for each zero in the whole
number power of 10.
Numbers 35 100 0 . 3 5
Dividing by Decimal Powers of 10 Move the decimal
point one place to the right for each decimal place in the
decimal power of 10.
Numbers 35 0.001 3 5 0 0 0 .
EXAMPLE
3
Divide Decimals Using Mental Math
a. 508.3 10 5 0 . 8 3 50.83
b. 508.3 0.01 5 0 8 3 0 . 50,830
Your turn now
5. 42.6 100
Move 1 place to the left.
Move 2 places to the right.
Find the quotient using mental math.
6. 509 1000
Lesson 4.5
7. 5 0.1
8. 3.2 0.001
Multiplying and Dividing by Powers of Ten
177
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
Vocabulary Use the numbers 10, 0.01, 100, and 0.1.
1. Which numbers are whole number powers of 10?
2. Which numbers are decimal powers of 10?
Find the product or quotient using mental math.
3. 7.58 10
4. 24.831 0.1
5. 16.35 0.01
6. 0.7 1000
7. 13.4 10
8. 27.65 100
9. 5.21 0.01
10. 3.108 0.1
11. Weaving The width of a tapestry
is 56.7 inches. The length of the
tapestry is 100 inches. Find the
area of the tapestry.
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
16–21, 28
36, 37
12–15, 22–27, 29
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Match the expression with its quotient.
12. 320.7 100
13. 320.7 10
A. 32.07
B. 3207
14. 320.7 0.01
C. 3.207
15. 320.7 0.1
D. 32,070
Find the product or quotient using mental math.
16. 3.9 10
17. 7.434 100
18. 459.8 0.001
19. 0.502 10,000
20. 4.9 0.1
21. 1000 0.01
22. 726.9 1000
23. 3.457 100
24. 82.93 10
25. 12.57 0.01
26. 0.9813 0.1
27. 0.31725 0.001
28. Alaska In 1999, the population of Alaska was 0.62 million. Write the
population as a whole number.
29. Microns A micron is a distance of 0.001 millimeter. An object has a
length of 87.2 millimeters. How many microns long is it?
Algebra Evaluate the expression.
178
Chapter 4
30. 8.3x, when x 1000
31. 3.75 x, when x 0.01
32. 5 x 0.02, when x 100
33. 6 x 34, when x 0.01
34. 50 8x, when x 0.001
35. 3.06x 21.5, when x 10
Decimal Multiplication and Division
Page 4 of 4
Ice Hockey The graph shows the number of people of different
ages who played ice hockey in 2000.
Sports
36. Find the number of
12–17 year olds that
played ice hockey
in 2000.
37. How many more 7–11
Ice Hockey Players in 2000
7–11 year olds
12–17 year olds
18–24 year olds
3.74
4.41
2.93
100,000 people
year olds played ice
hockey in 2000 than
18–24 year olds?
Number Sense Copy and complete the statement using <, >, or .
38. 532.4 0.001 _?_ 5.32
39. 12.22 0.01 _?_ 0.12
Challenge Tell whether the statement is true or false.
40. When you divide a whole number by a whole number power of 10, the
quotient is less than or equal to the dividend.
■
Ice Hockey
The Stanley Cup hockey
trophy is 35.5 inches tall and
weighs 32 pounds. About
how many trophies would it
take to equal the height of
your school? Do you think the
trophy weighs more than or
less than a bicycle?
41. When you divide a whole number by a decimal power of 10, the
quotient is less than the dividend.
Mixed Review
Find the sum or difference. (Lesson 3.6)
42. 5.5 4.8
43. 18.7 2.19
44. 6 3.4
45. 7.21 5.94
48. 6.02 3.7
49. 9.114 5.3
Find the product. (Lesson 4.3)
46. 7.5 6.8
47. 2.24 0.04
Basic Skills You give a salesclerk $15. Tell how much change
you should receive for the given purchase amount.
50. $12
51. $14.91
52. $11.58
53. $6.32
Test-Taking Practice
INTERNET
State Test Practice
54. Multiple Choice The price of one nail is $.01. If the price for a whole
box of the nails is $36.80, how many nails does the box contain?
CLASSZONE.COM
A. 37
B. 368
C. 3680
D. 36,800
55. Multiple Choice What is the product 43.64 0.1?
F. 0.4364
G. 4.364
Lesson 4.5
H. 43.64
I. 436.4
Multiplying and Dividing by Powers of Ten
179