Classifying Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers
Real Numbers
Whole numbers consist of any positive
number which does not have
fractional parts.
This set also includes zero.
0, 1, 2, 3, 4, 5, 6, 7, …
Fractions
Mixed Numbers
Negative Numbers
Integers are whole numbers both
positive and negative.
This set also includes zero.
…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …
Fractions
Mixed Numbers
Notice that the set of whole numbers
is included in the set of integers.
Integers
Whole
Numbers
Rational numbers include all integers
as well as terminating & repeating
decimals, fractions, and mixed
number.
…, -3,-2.75, -2, -1, 0, ½, .7, 1, 2, 3, 3.5 …
Nonterminating, nonrepeating decimals
What isn’t a rational number
These numbers are irrational. They
are nonrepeating, nonterminating
decimals.

Note: These are
square roots of
non-perfect
squares.
= 3.141592653…
2 = 1.414213562…
5
= 2.23606797…
Rational numbers include both integers and whole numbers.
Rationals
Integers
Whole
Numbers
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
.7
2)
-4
3)
2.75
4)
.3
5)
25
6)
-2½
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
.7
2)
-4
3)
2.75
4)
.3
5)
25
6)
-2½
rational
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
.7
rational
2)
-4
integer, rational
3)
2.75
4)
.3
5)
25
6)
-2½
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
.7
rational
2)
-4
integer, rational
3)
2.75 rational
4)
.3
5)
25
6)
-2½
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
.7
rational
2)
-4
integer, rational
3)
2.75 rational
4)
.3
5)
25
6)
-2½
rational
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
.7
rational
2)
-4
integer, rational
3)
2.75 rational
4)
.3
rational
5)
25
whole, integer, rational
6)
-2½
Classify each number as whole, integer, or rational. You
may give multiple names to each number.
1)
0.7
rational
2)
-4
integer, rational
3)
2.75 rational
4)
0.3
rational
5)
25
whole, integer, rational
6)
-2½
rational
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
Integers
Whole
Numbers
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
Integers
-5
Whole
Numbers
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
Integers
-5
Whole
Numbers
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
½
Integers
-5
Whole
Numbers
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
½
Integers
-5
Whole
Numbers
6/
1
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
½
Integers
-5
Whole
Numbers
6/
1
0
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
½
Integers
14
-5
Whole
Numbers
6/
1
0
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
½
Integers
14
-5
Whole
Numbers
6/
1
0
-4 ¾
Place the following numbers in the appropriate location on the diagram:
6/
-5
2.6
½
0
14
-4 ¾
4.0
1
Rationals
2.6
½
Integers
14
4.0
Whole
Numbers
6/
1
0
-4 ¾
-5
The set of rational numbers and irrational numbers
comprise the set of real numbers.
Rationals
Integers
Whole
Numbers
Real
Numbers
Irrationals
Decide whether each number is
rational or irrational.
1)
25
2)
30
3)
-6
4)  16
5) 2.4545454545…
6) 7.25
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30
3)
-6
4)  16
5) 2.4545454545…
6) 7.25
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
4)  16
5) 2.4545454545…
6) 7.25
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
rational
4)  16
5) 2.4545454545…
6) 7.25
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
rational
4)  16 rational
5) 2.4545454545…
6) 7.25
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
rational
4)  16 rational
5) 2.4545454545… rational
6) 7.25
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
rational
4)  16 rational
5) 2.4545454545… rational
6) 7.25 rational
7)
8
8)
40
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
rational
4)  16 rational
5) 2.4545454545… rational
6) 7.25 rational
7)
8
8)
40
irrational
Decide whether each number is
rational or irrational.
1)
25 rational
2)
30 irrational
3)
-6
rational
4)  16 rational
5) 2.4545454545… rational
6) 7.25 rational
7)
8
irrational
8)
40 irrational
What isn’t a real number
These “numbers” are NOT real
numbers.
9
15
 24
You cannot find the square root
of a negative number.
5
0
3
0
12
0
You cannot divide by zero.
Classify each number as
real or not real.
1)
 25
2)  64
3)
0
4
4)
8
5)
4
0
Classify each number as
real or not real.
1)
 25
2)  64
3)
0
4
4)
8
5)
4
0
Not real
Classify each number as
real or not real.
1)
 25
2)  64
3)
0
4
4)
8
5)
4
0
Not real
Real
Classify each number as
real or not real.
1)
 25
2)  64
3)
0
4
4)
8
5)
4
0
Not real
Real
Real
Classify each number as
real or not real.
1)
 25
2)  64
Not real
Real
3)
0
4
Real
4)
8
Not real
5)
4
0
Classify each number as
real or not real.
1)
 25
2)  64
Not real
Real
3)
0
4
Real
4)
8
Not real
5)
4
0
Not real
Whole Numbers
0
1
2
3
Integers
-3
-2
-1
0
1
2
3
Rational Numbers
-3
2
1
4
-2
-1 -.75
0
1
2
1
2 2 .3
3
Irrational Numbers
 14
 2
5
π
14
26
REAL NUMBERS =
Rational Numbers
-3
2
1
4
-2
-1 -.75
1
2
0
+
2 2 .3
1
Irrational Numbers
 14
 2
5
π
14
26
3
Give 2 examples of each kind of
number.
Rationals
Integers
Whole
Numbers
Real
Numbers
Irrationals
Numbers
that are NOT
real.