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Changing Decimals to Fractions

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Page 1 of 4
Changing Decimals to Fractions
BEFORE
Now
WHY?
You wrote decimals and
fractions.
You’ll write a decimal as a
fraction.
So you can find the miles you’ve
gone on a road trip, as in Ex. 7.
You can use models to write decimals as fractions.
Word Watch
1 Draw a model for 0.25. Each small
square represents one hundredth.
The shaded part represents
twenty-five hundredths.
Review Words
simplest form, p. 229
mixed number, p. 244
25
100
0.25 П­ бЋЏбЋЏ
2 Draw a model for 0.3. Each column
represents one tenth. The shaded part
represents three tenths.
3
10
0.3 П­ бЋЏбЋЏ
Use a model to write the decimal as a fraction.
1. 0.15
with
Solving
With practice, you will learn
to recognize the fraction
form of several common
decimals. Here are some
examples.
1
2
0.2 П­ бЋЏбЋЏ
1
4
3
0.75 П­ бЋЏбЋЏ
4
0.125 П­ бЋЏбЋЏ
1
8
2
5
0.4 П­ бЋЏбЋЏ
3. 0.4
4. 0.5
You can use decimal place value to help you write a decimal as a fraction
in simplest form.
one tenth
one hundredth
one thousandth
1
0.1 П­ бЋЏбЋЏ
10
1
0.01 П­ бЋЏбЋЏ
100
0.001 П­ бЋЏбЋЏ
1
5
0.5 П­ бЋЏбЋЏ
0.25 П­ бЋЏбЋЏ
2. 0.35
EXAMPLE
1
1
1000
Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
8
a. 0.8 П­ бЋЏ10бЋЏ
4
5
П­бЋЏ
36
бЋЏ
b. 0.36 П­ бЋЏ
100
9
25
П­ бЋЏбЋЏ
Write eight tenths as a fraction.
Simplify.
Write thirty-six hundredths as a fraction.
Simplify.
Lesson 5.7
Changing Decimals to Fractions
249
Page 2 of 4
EXAMPLE
Science
2
Writing Decimals as Mixed Numbers
Planets The length of a planet’s day
is the time it takes the planet to rotate
once about its axis. Write each length
as a mixed number in simplest form.
a. Length of day on Saturn: 10.5 hours
b. Length of day on Jupiter: 9.92 hours
axis
Solution
5
a. 10.5 П­ 10 бЋЏ10бЋЏ
1
2
П­ 10 бЋЏбЋЏ
Write ten and five tenths as a mixed number.
Simplify.
1
2
ANSWER The length of a day on Saturn is 10 бЋЏбЋЏ hours.
в– Planets
The length of a planet’s year
is the time it takes to revolve
once about the Sun. The
closer the planet is to the
Sun, the shorter its year. The
length of Jupiter’s year is
4330.6 Earth days. Saturn’s
year is 10,747 Earth days.
Which is closer to the Sun?
92
бЋЏ
b. 9.92 П­ 9 бЋЏ
100
23
25
П­ 9 бЋЏбЋЏ
Write nine and ninety-two hundredths as a
mixed number.
Simplify.
23
25
ANSWER The length of a day on Jupiter is 9 бЋЏбЋЏ hours.
EXAMPLE
3
Decimals with Zeros
Write the decimal as a fraction or mixed number in simplest form.
4
бЋЏ
a. 2.04 П­ 2 бЋЏ
100
1
25
П­ 2 бЋЏбЋЏ
608
бЋЏ
b. 0.608 П­ бЋЏ
1000
76
125
П­ бЋЏбЋЏ
Write two and four hundredths as a mixed number.
Simplify.
Write six hundred eight thousandths as a fraction.
Simplify.
Your turn now
Write the decimal as a fraction or mixed number in
simplest form.
1. 0.4
250
Chapter 5
Number Patterns and Fractions
2. 1.82
3. 2.005
4. 0.405
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 712
Getting Ready to Practice
1. Vocabulary Explain how you know a fraction is in simplest form.
2. Find the Error Describe
7
100
and correct the error in
the solution.
0.7 П­ бЋЏбЋЏ
Copy and complete the statement.
?
3. 0.27 П­ бЋЏбЋЏ
100
3
4. 2.3 П­ 2 бЋЏбЋЏ
?
?
5. 6.2 П­ 6 бЋЏбЋЏ
10
23
6. 5.23 П­ 5 бЋЏбЋЏ
?
7. Road Trip At your first stop during a road trip, you record the distance
you’ve traveled as 128.4 miles. How could you write this distance as a
mixed number in simplest form?
Practice and Problem Solving
Write the number as a decimal and as a fraction or mixed number.
8. nine tenths
9. fifty-three hundredths
10. two and seven tenths
11. three and eleven hundredths
Write the decimal as a fraction or mixed number in simplest form.
with
Homework
Example Exercises
1
8–9, 12–13,
24–26
2
10–11, 14–15
3
16–23
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial plus
12. 0.16
13. 0.72
14. 5.9
15. 9.3
16. 4.06
17. 3.01
18. 0.902
19. 0.806
20. 0.039
21. 0.025
22. 6.036
23. 9.401
In Exercises 24–26, use the graph.
The graph shows the portion of space in a
mall occupied by different types of stores.
The portions are written as decimals.
24. Which type of store occupies the least
space in the mall? the most?
25. Use the circle graph to order the types
Mall Space by Store Type
Clothing
0.48
Food 0.19
Gifts 0.18
Electronics
0.10
Furniture
0.05
of stores by the portion of space
they occupy.
26. Write the decimals from Exercise 25 as fractions in order from
least to greatest.
Lesson 5.7
Changing Decimals to Fractions
251
Page 4 of 4
27. Honeybee A bee has a length of approximately 0.4708 inch. Write the
bee’s length as a fraction in simplest form.
28. Rainfall The normal monthly precipitation for New Orleans is
4.50 inches in April and 3.05 inches in October. Write the difference of
these amounts as a mixed number in simplest form.
Challenge Write the decimal as an improper fraction in simplest form.
29. 2.37
30. 6.95
31. 9.86
32. 5.34
Mixed Review
Divide. Round your answer to the nearest tenth, if necessary.
(Lesson 4.4)
33. 8 П¬ 11
34. 6 П¬ 12
35. 3 П¬ 5
36. 5 П¬ 9
5 1 11
13
37. Order the fractions бЋЏбЋЏ, бЋЏбЋЏ, бЋЏбЋЏ, and бЋЏбЋЏ from least to greatest. (Lesson 5.5)
6 2 36
18
Choose a Strategy Use a strategy from
the list to solve the following problem.
Explain your choice of strategy.
Problem Solving Strategies
Guess, Check, and Revise
Draw a Diagram
в– Perform an Experiment
в– Work Backward
в– в– 38. You have 2 photographs that are the
same size. How many ways can you
arrange them (face up and right-side up)
next to each other to form a rectangle
with twice the area of one photo?
Basic Skills Copy and complete the statement.
39. 5 hours П­ _?_ minutes
40. 367 minutes П­ _?_ hours _?_ minutes
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
41. Multiple Choice Which fraction is equivalent to the decimal 0.24?
1
A. бЋЏ24бЋЏ
3
B. бЋЏ25бЋЏ
6
C. бЋЏ25бЋЏ
12
D. бЋЏ25бЋЏ
42. Multiple Choice A survey at a middle school said that 0.65 of the sixth
grade students named basketball as their favorite sport. Which fraction
represents the decimal 0.65?
3
5
F. бЋЏбЋЏ
252
Chapter 5
Number Patterns and Fractions
13
20
G. бЋЏбЋЏ
7
10
H. бЋЏбЋЏ
3
4
I. бЋЏбЋЏ
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