NAME ______________________________________________ DATE ______________ PERIOD _____
9-2
Study Guide and Intervention
The Real Number System
The set of real numbers consists of all natural
numbers, whole numbers, integers, rational
numbers, and irrational numbers.
Rational
Numbers
1
8
• Rational numbers can be written as fractions.
1
0
• Irrational numbers are decimals that do not
repeat or terminate.
0.64
Example
Integers
Irrational
Numbers
0.4
Whole 5
Numbers
0.7
Natural
Numbers
1 3
3
1
2
0.121221222...
Name all of the sets of numbers to which each real number belongs.
a. 7
This number is a natural number, a whole number, an integer, and a rational number.
b. 0.6
2
3
This repeating decimal is a rational number because it is equivalent to .
c. 71
It is not the square root of a perfect square so it is irrational.
81
3
d. 81
3
Since = –27, this number is an integer and a rational number.
e. 169
Because 169
= –13, this number is an integer and a rational number.
Exercises
Name all of the sets of numbers to which each real number belongs. Let
N natural numbers, W whole numbers, Z integers, Q rational numbers,
and I irrational numbers.
1. 21
N, W, Z, Q
8
12
3. Q
4. 5 Z, Q
5. 17
N, W, Z, Q
6. O W, Z, Q
7. 0.257 Q
8. 0.9
Q
9. 78
1
4
10. Q
13. 5.7
©
3
7
2. I
Q
Glencoe/McGraw-Hill
11. I
14. 8.5
N, W, Z, Q
12. 169
Z, Q
15. 289
Z, Q
Q
494
Glencoe Pre-Algebra
NAME ______________________________________________ DATE ______________ PERIOD _____
9-2
Skills Practice
The Real Number System
Name all of the sets of numbers to which each real number belongs. Let
N natural numbers, W whole numbers, Z integers, Q rational numbers,
and I irrational numbers.
1. 12
N, W, Z, Q
2. 25
1
8
3. 5 Z, Q
N, W, Z, Q
1
9
4. Q
5. Q
6. 0.343434. . . Q
7. 31
I
8. 7
I
9. 32
4
10. 13. 418
Z, Q
11. 6.54
N, W, Z, Q
25
5
Q
12. 24.6
14. 0 W, Z, Q
N, W, Z, Q
Q
15. 0.050050005 . . . I
Determine whether each statement is sometimes, always, or never true.
Lesson 9-2
16. A whole number is a rational number. always
17. A rational number is a natural number. sometimes
18. A negative number is an integer. sometimes
19. Zero is a natural number. never
Replace each with , , or to make a true statement.
3
7
20. 4
2 22. 12
3.5
21. 5
2.1
23. 104.0
4
10.2
24. 7.8 55
25. 15.1 231
Order each set of numbers from least to greatest.
1
3
1
4
1
4
1
3
26. 5 , 5.3, 28
, 2 2, 28
, 5.3, 5 1 36
4 5
27. 53
, 7 , , 7.27
36
1
, 7 , 7.27, 53
5
4
2
10
2
10
28. 9.35, 72.25
, 9 , 9 9.35, 9 , 9, 72.25
ALGEBRA Solve each equation. Round to the nearest tenth, if necessary.
29. a2 64
8
32. 76 g2 8.7
35. b2 4.41
©
2.1
Glencoe/McGraw-Hill
30. d 2 169
13
33. 115 h 2 10.7
36. y 2 0.36
0.6
495
31. f 2 441
21
34. k 2 450
21.2
37. m 2 0.0025 0.05
Glencoe Pre-Algebra