Changing Decimals to Fractions Now

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


2 Draw a model for 0.3. Each column represents one tenth. The shaded part represents three tenths. 3 10

0.3


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


1 4 3 0.75
 4

0.125


1 8

2 5

0.4


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
 10

1 0.01
 100

0.001


1 5

0.5
 0.25


2. 0.35

EXAMPLE

1

1 1000

Writing Decimals as Fractions

Write the decimal as a fraction in simplest form. 8

a. 0.8
10 4 5




36

 b. 0.36
 100 9 25




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
10 10 1 2


10 

Write ten and five tenths as a mixed number. Simplify. 1 2

ANSWER The length of a day on Saturn is 10  hours. ■

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

 b. 9.92
9  100 23 25


9 

Write nine and ninety-two hundredths as a mixed number. Simplify. 23 25

ANSWER The length of a day on Jupiter is 9  hours.

EXAMPLE

3

Decimals with Zeros

Write the decimal as a fraction or mixed number in simplest form. 4

 a. 2.04
2  100 1 25


2  608

 b. 0.608
 1000 76 125




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


Copy and complete the statement. ? 3. 0.27
 100

3 4. 2.3
2  ?

? 5. 6.2
6  10

23 6. 5.23
5  ?

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  11

34. 6  12

35. 3  5

36. 5  9

5 1 11 13 37. Order the fractions , , , and  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 ■ Perform an Experiment ■ Work Backward ■ ■

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
_?_ minutes

40. 367 minutes
_?_ 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. 24

3

B. 25

6

C. 25

12

D. 25

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. 

252

Chapter 5

Number Patterns and Fractions

13 20

G. 

7 10

H. 

3 4

I.