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Is It a Bird or a Plane?Rational Numbers

VocabularyDefine each set of numbers in your own words.

1. Natural numbers Natural numbers consists of the numbers that you use to count objects.

2. Whole numbers Whole numbers are made up of the set of natural numbers and the number 0.

3. Integers Integers include all of the whole numbers and their additive inverses.

4. Closed A set of numbers is said to be closed when the operations could produce a defined

value that is also in the set.

5. Rational numbers Rational numbers are numbers that can be written in the form a__ b

, where a and

b are both integers and b is not equal to 0.

Problem SetWrite each fraction as a decimal.

1. 1 __ 4

5 0.25 2. 5 __ 8

5 0.625

3. 23 ____ 100

5 0.23 4. 1 2 __ 5

5 1.4

5. 3 7 ___ 16

5 3.4375 6. 12 15 ___ 32

5 12.46875

Graph each pair of rational numbers on the number line. Use the graph and write ., ,, or 5 to

compare the numbers.

7. 3 __ 5

. 0.25

0 0.2 0.3

0.25

0.4 0.5 0.6 0.7 0.8 0.9 1.00.1

35

8. 1.7 . 1 5 __ 8 1.7

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

58

1

Lesson 5.1 Skills Practice

Name ________________________________________________________ Date _________________________

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Lesson 5.1 Skills Practice page 2

9. 0.09 , 9 ___ 10

0 0.2 0.3

0.09

0.4 0.5 0.6 0.7 0.8 0.9 1.00.1

910

10. 4 3 __ 4 . 4.34 4.34

5.04.14.0 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9

344

11. 11 ___ 16

. 0.65

0 0.2 0.3

0.65

0.4 0.5 0.6 0.7 0.8 0.9 1.00.1

1116

12. 3.8 5 3 4 __ 5

3.8

4.03.13.0 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

45

3

Tell whether the numbers in each problem are natural numbers, whole numbers, or integers, and

identify whether those numbers are closed or open under the operation used.

13. 23 1 18 5 41

natural numbers, whole numbers, or integers; closed under addition

14. 35 3 0 5 0

whole numbers or integers; closed under multiplication

15. 4 2 (23) 5 7

integers; closed under subtraction

16. 0 2 5 5 25

whole numbers are not closed under subtraction; closed under subtraction as integers

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Lesson 5.1 Skills Practice page 3

Name ________________________________________________________ Date _________________________

17. 9 2 11 5 22

natural numbers or whole numbers are not closed under subtraction; closed under subtraction

as integers

18. 212 4 (25) 5 2 2 __ 5

integers; not closed under division

Add, subtract, multiply, or divide the rational numbers in each.

19. 27 1 13 5 6 20. 1 ___ 10

1 3 __ 5

5 7 ___ 10

21. 4 1 __ 2

2 2 3 __ 8 5 2 1 __

8 22. 21.44 4 0.12 5 212

23. 2.40 3 (23.75) 5 29 24. 6 __ 5

3 ( 2 7 ___ 12 ) 5 2 42 ___ 60

5 2 7 ___ 10

25. 5 __ 3

4 1 __ 4

5 20 ___ 3

5 6 2 __ 3

26. 12.7 2 39.6 5 226.9

27. 27.82 2 (25.09) 5 22.73 28. 2 4 __ 9 4 ( 2 32 ___ 27 ) 5 3 __ 8

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Chapter 5      Skills Practice      •      527

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Sew What?Irrational Numbers

VocabularyMatch each term with the number that represents that term.

1. Irrational number a. 1 __ 2

5 0.5

c

2. Terminating decimal b. 0. __

3

a

3. Repeating decimal c. π

d

4. Bar notation d. 5 __ 9

5 0.555…

b

Problem SetConvert each fraction to a decimal and tell whether the fraction results in a terminating or repeating

decimal.

1. 1 ___ 25

2. 7 __ 9

0.04 0.7 __

7 25 )

_____ 1.00 ; terminating 9 )

_____ 7.00 ; repeating

3. 5 ___ 12

4. 5 __ 8

0.416 __

6 0.62512 )

_______ 5.0000 ; repeating 8 )

______ 5.000 ; terminating

5. 13 ___ 16

6. 8 ___ 11

0.8125 0. ___

72 16 )

________ 13.0000 ; terminating 11 )

_____ 8.00 ; repeating

Lesson 5.2 Skills Practice

Name ________________________________________________________ Date _________________________

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Lesson 5.2 Skills Practice page 2

Write each repeating decimal as a fraction.

7. 0.333 … 8. 0.888 …

10w 5 3.33... 10w 5 8.88...

2w 5 0.33... 2w 5 0.88...

9w 5 3 9w 5 8

w 5 3 __ 9

5 1 __ 3

w 5 8 __ 9

9. 0.0707 … 10. 0.5454 …

100w 5 7.07... 100w 5 54.54...

2w 5 0.07... 2w 5 0.54...

99w 5 7 99w 5 54

w 5 7 ___ 99

w 5 54 ___ 99

5 6 ___ 11

11. 0.1515 … 12. 0.2727 …

100w 5 15.15... 100w 5 27.27...

2w 5 0.15... 2w 5 0.27...

99w 5 15 99w 5 27

w 5 15 ___ 99

5 5 ___ 33

w 5 27 ___ 99

5 3 ___ 11

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Lesson 5.2 Skills Practice page 3

Name ________________________________________________________ Date _________________________

13. 0.298298 … 14. 0.185185 …

1000w 5 298.298... 1000w 5 185.185...

2w 5 0.298... 2w 5 0.185...

999w 5 298 999w 5 185

w 5 298 ____ 999

w 5 185 ____ 999

5 5 ___ 27

15. 0.67896789… 16. 0.0243902439 …

10,000w 5 6789.6789... 100,000w 5 2439.02439...

2w 5 0.6789... 2w 5 0.02439...

9999w 5 6789 99,999w 5 2439

w 5 6789 _____ 9999

5 2263 _____ 3333

w 5 2439 _______ 99,999

5 1 ___ 41

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Lesson 5.2 Skills Practice page 4

Tell whether each number is rational or irrational.

17. π 18. √__

4

irrational rational (2)

19. √___

18 20. 3  27

irrational rational (3)

21. 3  30 22. √__

1 ____ √

___ 49

irrational rational ( 1 __ 7

)

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Worth 1000 WordsReal Numbers and Their Properties

VocabularyWrite a description of each term in your own words.

1. real numbers: The set of real numbers is the combined set of rational numbers and irrational

numbers.

2. Venn diagram: A Venn diagram is a diagram used to show how sets overlap.

3. closed (under an operation): A set of numbers is closed under an operation if the result of the

operation on two numbers in the set is another member of the set.

Problem SetIndicate whether each real number shown is rational, irrational, an integer, a whole number, a natural

number, or some combination.

1. 35 2. √___

17

rational, integer, whole irrational

number, natural number

3. 26 4. 5.25

rational, integer rational

5. √___

81 6. 2 2 __ 3

rational, integer, whole rational

number, natural number

Lesson 5.3 Skills Practice

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Lesson 5.3 Skills Practice page 2

7. 14 ___ 5

8. 0 __ 7

rational rational, integer, whole number

9. 3  9 10. 2 √

___ 16 ____

3  8

irrational rational, integer

Identify the property represented in each problem.

11. 18 3 1 5 18 12. 87 1 (259) 5 259 1 87

multiplicative identity commutative property of addition

13. 174 1 (2174) 5 0 14. If 1 __ 2

1 1 __ 2

5 1 and 4 ( 1 __ 4

) 5 1 then 1 __ 2

1 1 __ 2

5 4 ( 1 __ 4 )

additive inverse transitive property of equality

15. 213 3 21 5 21 3 (213) 16. 2365 1 0 5 2365

commutative property of additive identity

multiplication

17. 3 1 __ 3 3 0.3 5 1 18. 245 1 (232 1 87) 5 [245 1 (232)] 1 87

multiplicative inverse associative property of addition

19. 567 5 567 20. If 2 3 __ 4 5 20.75 then 20.75 5 2 3 __ 4 .

reflexive property of equality symmetric property of equality

21. [5 3 (23)] 3 12 5 5 3 [(23) 3 12] 22. 2 4 __ 5 1 0.8 5 0

associative property of multiplication additive inverse