Notes Z Section 4.2

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Number, Relations & Functions 10 Z
Section 4.2
Classifying Numbers
NATURAL NUMBERS: The set of natural numbers consists of the numbers that you use to count objects.
(1, 2, 3, 4, 5, …)
WHOLE NUMBERS: The set of whole numbers consists of the set of natural numbers and the number 0. (0, 1, 2, 3, 4, …)
INTEGERS: The set of integers consists of the set of whole numbers and their opposites. (…,-3, -2, -1, 0, 1, 2, 3, …)
RATIONAL NUMBERS: The set of rational numbers consists of all numbers that can be written as
a
, where a and b are
b
 10 2 0 4 7 9 
, , , , ,

5
3 6 2 4 3 

integers, but b is not equal to 0. Examples:  
IRRATIONAL NUMBERS: The set of irrational numbers consists of all numbers that cannot be written as
a
, where a and
b
b are integers. Examples:  , 7, 15 , 1.487299031…
REAL NUMBERS: The set of real numbers consists of the set of rational numbers and irrational numbers.
Exercise: Classify each of the following numbers by writing them in the correct location on the
diagram below. Write each number only once.
22
14
9
3  5 0.25
Natural
Number
ss
7
0.2713
10
7
2  25
7
Number, Relations & Functions 10 Z
Section 4.2
Table of Squares, Cubes, Perfect Fourths, and Perfect Fifths
x
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
x2
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
x3
1
8
27
64
125
216
343
512
729
1,000
1,331
1,728
2,197
2,744
3,375
4,096
4,913
5,832
6,859
8,000
9,261
10,648
12,167
13,824
15,625
x4
1
16
81
256
625
1,296
2,401
4,096
6,561
10,000
14,641
20,736
28,561
38,416
50,625
65,536
83,521
104,976
130,321
160,000
194,481
234,256
279,841
331,776
390,625
x5
1
32
243
1,024
3,125
7,776
16,807
32,768
59,049
100,000
161,051
248,832
371,293
537,824
759,375
1,048,576
1,419,857
1,889,568
2,476,099
3,200,000
4,084,101
5,153,632
6,436,343
7,962,624
9,765,625
Number, Relations & Functions 10 Z
Section 4.2
EXERCISE
1. Answer true or false for each statement.
a. Real numbers are either rational or irrational. ___________________
b. An irrational number can be a repeating decimal. ________________
c. All whole numbers are natural numbers. _______________________
d. Irrational numbers are not real numbers. ______________________
e. All natural numbers are integers. ____________________________
f. The fraction ½ can be written as a terminating decimal. ___________
g. All integers are rational numbers. _____________________________
2. Write a number that is
a. a rational number but not an integer. _________________________
b. a whole number but not a natural number. _____________________
c. an irrational number. ______________________________________
3. Check all the classifications that apply to each real number.
Number
Natural
Whole
Integer
Rational
Irrational
Real
49
7
11
10
0
2
6
54
6
 196
4. Compare the following numbers using > or <.
a.
32
5.1
d.
17
b.
99
28
3
e.
65
c.
16
3.9
f.
50
9
2
43
5
15
2
g.
38
42
h.
17
4.2
i.
2
7
4
5. Place a point on the number line given for each of the following irrational numbers.
Point A:
2
Point B:
17
Point C:
11
Point D:
8
Point E:
5
Number, Relations & Functions 10 Z
Section 4.2
6. Place a point on the number line for each of the following irrational numbers.
Point V:
26
Point W:
88
Point X:
77
Point Y:
37
Point Z:
7. Name the point on the number line associated with each irrational number.
50
103
62
90
37
8. Name the point on the number line associated with each irrational number.
7
22
34
38
15
9. List the following numbers in order from least to greatest.
a.
b.
c.
11
,  , 2.98,  7
5
7
, 11,  16, 3.3,  36
2
 49,  7,0,  51, 6.8
d.
e.
f.
4,
49
18
,1.2,
36
5
 8, 3.1, 15,(2)2 ,  11
1 1 2 3
, , ,
2 3 3 4
30
Number, Relations & Functions 10 Z
10. Graph each set of numbers on a number line.
a. 4.8, 17,  8, 4.2, 25
b.  5,
c.
 
5
, ,4 , 18
2 3 8
3 1
5
,
,0.46,
7 2
6
d.  10,
e.
3
 3
, ,0.81
2 4
92, 3 169, 3 54 , 3 35
Section 4.2

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