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Sets of Numbers in the Real Number System
Reals A real number is either a rational number or an irrational number. 2 4, −7, 0, , 11 3

Rationals A rational number is any number that p can be put in the form where p q and q are integers and q ≠ 0 . 12 5 1 8 3, , − , 4 , 6 2 7 13

Irrationals

An irrational number is a nonrepeating, nonterminating decimal.
2, π, − 3 7, 0.121231234 . . ., 13Non-Integer Fractions A non-integer fraction is a fraction whose numerator is not a multiple of the denominator. 1 5 3 , − ,8 2 4 7

Integers The integers consist of the natural numbers, 0, and the opposites of the natural numbers. . . . –2, –1, 0, 1, 2, 3, . . .

. . . –5, –4, –3, –2, –1

Whole Numbers The whole numbers consist of the natural numbers and 0. 0, 1, 2, 3, 4, . . .

0Natural Numbers The natural numbers are also referred to as the counting numbers. 1, 2, 3, 4, . . .

23

Real Number System Worksheet

24

The Number System
Identify the sets to which each of the following numbers belongs by marking an “X” in the appropriate boxes. Number 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Natural Numbers Whole Numbers Integers Rational NumbersIrrational Numbers Real Numbers

− 17

−2
− 9 37
0

− 6.06

4.5 6

3.050050005...
18

− 43 0

π
.634

225
.634

4 49

− 64

25

Number 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Irrational Numbers

Real Numbers

13
−5

2 3
−0.083
27

2.647 3.0505
−198

−

1 2

10

ANSWERS 1. IN, R 3. RN, R5. RN, R 7. IN, R 9. None 11. RN, R 13. RN, R 17. I, RN, R 19. RN, R 21. RN, R 23. I, RN, R 25. N, W, I, RN, R 15. I, RN, R

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The Real Number Line Worksheet
Graph the number on the real number line. 1. 3

1 2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

2. -2

1 2

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

3. - 4.5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

4. 0.5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

5.17
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

6. - 10
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

7. - 24
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

8.

15
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Graph. 9. the real numbers greater than 4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

10. the real numbers greater than 1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

11. the real numbers less than 0
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

12. thereal numbers greater than -2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

13. the real numbers less than -3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

14. the real numbers less than 5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

15. the real numbers less than - 4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

16. the real numbers less than -2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

17. the real numbers between 2 and 6
-6 -5 -4 -3 -2 -10 1 2 3 4 5 6

18. the real numbers between -3 and 1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

19. the real numbers between -5 and -1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

20. the real numbers between -3 and 0
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

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Solve. 21. For the inequality x ≥ 6, which numbers listed below make the inequality true?

a. -2.6

b. 0

c. 6

d.

83

22. For theinequality x < 3, which numbers listed below make the inequality true?

a. - 21

b. 0

c. 3

d. 3.02

23. For the inequality x ≤ -5, which numbers listed below make the inequality true?

a. 6

b. -5

c. 0

d. - 5

24. For the inequality x ≥ -2, which numbers listed below make the inequality true?

a. -5

b. -2

c. -1.6

d.

3

What values of the variable x make theinequality true? 25. x > 4 26. x < -3 27. x ≤ -6 28. x ≥ 2

Graph the inequality on the real number line. 29. x > -3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

30. x < 5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

31. x ≥ 0
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

32. x ≤ - 4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

33. x < -1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

34. x ≥ 3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

35. x ≤ 1
-6 -5...