Objective - To recognize, graph, and compare
rational numbers.
Rational Number - any number that can be written
1
3
as a fraction. ie :
, 5
7
3
31
9
including decimals... ie : 0 .9 
,  2.31   2
100
10
17
4
including decimals ie : 0 .4  ,  5.17   5
99
9
that repeat...
62
5
including Integers... ie :  5   , 62 
1
1
0
13
, 0 
including Wholes... ie : 1 3 
2
1
Rational Numbers
Fractions/Decimals
3
1
2 .5 , 3 ,  ,  0 .4 5
7
5
Integers
…-3, -2, -1, 0, 1, 2, 3…
Negative Integers
…-3, -2, -1
Zero
0
Wholes
0, 1, 2, 3...
Naturals
1, 2, 3...
Create a Venn Diagram that shows the relationships
between the following sets of numbers.
Naturals, Wholes, Integers, Rationals
 0 .4 5
Rationals
Integers
3

7
1
3
5
-3
-47
Wholes
Naturals
1, 2, 3...
0
2 .5
Identify all of the sets to which each number
belongs. (Naturals, Wholes, Integers, Rationals)
1) -6 Integer, Rational
2)  5
7
8
Rational
3) 14 Natural, Whole, Integer, Rational
4) 0.8 Rational
Identify all of the sets to which each number
belongs. (Naturals, Wholes, Integers, Rationals)
1) 0
Whole , Integer, Rational
2) - 2.03 Rational
3)
2
1
5
4)
0 .8
Rational
Rational
Show that each number below is Rational by writing
it as a fraction in the form a , w here b  0.
b
17
1) 17 
1
8
5)  8  
1
23
3
2) 5 
4
4
33
233
6) 2.33  2

100
100
89
3) 0.89 
100
5
1
 1
7 )  1.5   1
10
2
4
4 ) 0 .4 
9
6
8)  6  
1
Comparing Rational Numbers in Decimal Form
Use < or > to compare.
1) 8.45987 < 8.51
8.45987
8.51
2) 0.3 < 0.335
0.33333...
0.335
3) 14.2 > 1.538
14.2
0 1.538
Comparing Rational Numbers in Fraction Form
Use < or > to compare the fractions below.
 
7 4
1)
7 5
>


7
5
5
5
 
2 5
3)
2 8
>

9 1
16 1
28
25
10
9
35
35
16
16

3 3
2)
3 11
<
 
1 11
3 11

3 5
4)
3 12
<
 
4 4
9 4
9
11
15
16
33
33
36
36
Graph the fractions below on a number line, then
order them from least to greatest.
7
3
,
5
, 
1
2
1


3
5
1

3
1
1
1
3
,
9
1
9
1
3
5
1
0
2
,
1
1
9
,
3
5
2
,
7
5
7
5
1
1
1
2
Graphing Rational Numbers on a Number Line
Graph the following numbers on a number line.
3
-4
-3
3
1
1
5
2
3
-2
1
1
2
-1
 0 .4
0
 0.4
1
3 .2 1
2
5
3
3
3 .2 1
4
4
W hich is greater 0.58 or ?
7
1
4
2
85 7
0
5
7
4
0.58
7 4.0000000
7
40
35
35
50
50
49
0.58
49
> 0.571428
10
1
7
30
28
All rational numbers either
20
terminate or repeat when
14
changed to a decimal.
60
56
Density
Rational numbers are infinitely dense.
This implies that between any two rational
numbers, an infinite number of other rational
numbers exist.
1 1 1
1
2
01 6 8 4
1
1
32
1
64