Page 1 of 5
Fractions and Decimals
BEFORE
Now
WHY?
You wrote decimals and
fractions.
You’ll write fractions as decimals
and decimals as fractions.
So you can compare the lengths of
marsupials, as in Ex. 45.
In the Real World
Word Watch
terminating decimal, p. 191
repeating decimal, p. 191
Geography The map gives the areas of the four largest states as fractions
of the total area of the United States. What is the order of the states from
greatest to least area? This question will be answered in Example 4.
Montana
1
25
Alaska
1
6
California
17
400
Texas
9
125
EXAMPLE
with
Review
Need help with dividing
decimals? See p. 67.
1
Writing Fractions as Decimals
7
20
5
8
Write (a) and (b) 3 as decimals.
Solution
a.
0.35
0
.0
207
60
100
100
0
b.
Write zeros in
dividend as
placeholders.
Remainder is zero.
7
20
ANSWER 0.35
Your turn now
3
1. 10
190
Chapter 4
Number Patterns and Fractions
0.625
85
0
.00
48
20
16
40
40
0
Write zeros in
dividend as
placeholders.
Remainder is zero.
5
8
ANSWER 3 3 0.625 3.625
Write the fraction or mixed number as a decimal.
17
2. 200
4
3. 3 5
7
4. 2 8
Page 2 of 5
Terminating and Repeating Decimals When a long division problem
results in a remainder of 0, the quotient is a terminating decimal .
Sometimes, long division gives a repeating decimal , where one or more
digits repeat without end. Repeating decimals can be written with a bar
over the digit(s) that repeat.
0.4444. . . 0.4
3.0505. . . 3.05
EXAMPLE
2
One digit repeats.
Two digits repeat.
Writing Fractions as Repeating Decimals
5
3
13
33
Write (a) and (b) as decimals.
Solution
a.
1.666. . .
35
.0
0
0
3
20
18
20
18
20
18
2
b.
The digit
6 keeps
repeating.
Remainder will
never be zero.
5
3
Review
Need help with place
value? See p. 52.
The digits
3 and 9 keep
repeating.
Remainder will
never be zero.
13
33
ANSWER 1.6
with
0.3939. . .
3
.0
0
0
0
331
99
310
297
130
99
310
297
13
ANSWER 0.39
To write a decimal as a fraction, use the place value of the last digit of the
decimal to determine the denominator. For example, to write 0.45 as a
45
100
fraction, use the fact that 5 is in the hundredths’ place and write .
EXAMPLE
3
Writing Decimals as Fractions
Write (a) 0.85 and (b) 4.375 as a fraction or mixed number.
Solution
85
a. 0.85 100
1
17 p 5
20 p 5 1
5 is in the
hundredths’
place.
375
b. 4.375 4 1000
17
20
1
3 p 125
8 p 125 1
4 5 is in the
thousandths’
place.
3
8
4 Lesson 4.7
Fractions and Decimals
191
Page 3 of 5
EXAMPLE
with
Solving
4
Ordering Numbers
To order the four largest states from page 190, you can write the fractions
as decimals and then compare the decimals.
Only the digit(s) under the
bar should be repeated. In
Example 4, Alaska’s area
compared with the area of
the U.S. is as a decimal,
0.16 0.1666. . . ,
not 0.1616. . . .
1
6
Alaska: 0.16
1
25
Montana: 0.04
17
400
California: 0.0425
9
125
Texas: 0.072
ANSWER Because 0.16
> 0.072 > 0.0425 > 0.04, the states are, from greatest
to least area, Alaska, Texas, California, and Montana.
Your turn now
7
5. 9
Write the fraction or mixed number as a decimal.
13
6. 6
5
7. 2 11
3
8. 4 22
Write the decimal as a fraction or mixed number in simplest form.
9. 0.4
10. 2.65
11. 1.0025
12. 0.735
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 708
Getting Ready to Practice
1. Vocabulary What is the difference between a terminating decimal and
a repeating decimal?
Write the fraction or mixed number as a terminating or repeating decimal.
1
2. 2
1
3. 1 4
1
4. 1 3
5
5. 6
2
6. 2 3
2
7. 2 5
3
8. 4
4
9. 3 9
Write the decimal as a fraction or mixed number in simplest form.
10. 0.6
11. 1.25
12. 0.2
13. 0.125
14. Rainbow Bridge At 88.4 meters, Rainbow Bridge in Utah is the highest
natural bridge in the world. Write the height as a mixed number in
simplest form.
192
Chapter 4
Number Patterns and Fractions
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
4
Homework
Exercises
19–26, 47–50
19–30, 47–50
31–38
40–43
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Match the number with its graph on the number line.
1
16. 2 4
15. 1.75
A
6
17. 5
B
1.0
C
1.5
18. 1.3
D
2.0
2.5
Write the fraction or mixed number as a decimal. Then tell whether
the decimal is a terminating decimal or repeating decimal.
3
19. 5
7
20. 6
5
21. 18
7
22. 7 8
9
23. 7 20
1
24. 2 9
7
25. 12
4
26. 5 25
Rewrite the repeating decimal using bar notation.
27. 0.7777. . .
28. 5.2121. . .
29. 3.5888. . .
30. 2.358358. . .
Write the decimal as a fraction or mixed number.
31. 0.8
32. 0.12
33. 0.475
34. 1.375
35. 6.24
36. 4.175
37. 2.245
38. 1.78
3
39. Writing If you were comparing 5 and 5.75, would you change the
5
mixed number to a decimal or the decimal to a mixed number? Why?
Order the numbers from least to greatest.
2
5
40. , 0.25, , 0.2, 0.2
7
2
4 2 16
41. 3.67, 3 , 3 , , 3.67
5 3 5
8
9 4
42. , 1.9, 1.94, , 1 3
4 9
9
6
15
43. , 0.89, , 0.90
, 10
7
20
44. Critical Thinking If you are using division
to write a fraction as a decimal, how do
you know when to stop dividing?
Numbat
45. Marsupials Koalas, numbats, and wombats
5
are marsupials. A koala is about feet long.
2
4
A numbat is about feet long. A wombat
3
63
is about feet long. Write the
20
three lengths as decimals.
Koala
Lesson 4.7
Fractions and Decimals
193
Page 5 of 5
46. Surface Area of Earth The total surface area of Earth (including land
and water) is about 510,000,000 square kilometers. The total land area
is about 150,000,000 square kilometers. Write a fraction that compares
the land area with the total surface area of Earth. Write the fraction as a
decimal to the nearest thousandth.
with
Notetaking
If you find that you are
having trouble writing a
fraction as a decimal,
write a question mark
next to the problem
and remember to ask
someone to explain it
to you.
Write the fraction or mixed number as a decimal. Then tell whether
the decimal is a terminating decimal or repeating decimal.
16
47. 5 37
29
48. 25
7
50. 9 111
55
49. 32
1 2
3
51. Number Sense Find the decimal forms of , , and . Predict the
9 9
9
4 5
6
decimal forms of , , and . Explain how you made your predictions.
9 9
9
52. Challenge What is true about the denominator of any fraction whose
decimal form terminates rather than repeats?
Mixed Review
Write the number in standard form. (Lesson 2.5)
53. 4.9 10 5
54. 5.358 10 2
55. 3.7743 10 8
Write the improper fraction as a mixed number. (Lesson 4.6)
16
56. 5
56
57. 9
23
58. 12
Basic Skills Solve the following problem.
59. Find how much time has elapsed between 12:44 P.M. and 9:36 P.M.
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
60. Multiple Choice There were 60 students who tried out for the school
play. Only 0.7 of the students were selected to be in the play. What
fraction of the students were not selected to be in the play?
1
20
A. 7
60
B. 3
10
C. 7
10
D. 61. Multiple Choice You collect stamps from all over the world, and
3
of your stamps are from the United States. What decimal represents
5
the portion of stamps from the United States?
F. 0.25
194
Chapter 4
Number Patterns and Fractions
G. 0.35
H. 0.4
I. 0.6