Download Objective - To recognize, graph, and compare rational numbers.

Objective - To recognize, graph, and compare
rational numbers.
Rational Number - any number that can be written
1
3
as a fraction. ie :
, 5
3
7
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 : 13 
2
1
Rational Numbers
Fractions/Decimals
3
1
2.5, 3 ,  , 0.45
5 7
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
0.45
Rationals
Integers
3

7
-47
1
3
5
2.5
-3
Wholes
Naturals
1, 2, 3...
0
Identify all of the sets to which each number
belongs. (Naturals, Wholes, Integers, Rationals)
1) -6 Integer, Rational
7
2) 5
Rational
8
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
2
3) 1
5
Rational
4) 0.8 Rational
Show that each number below is Rational by writing
it as a fraction in the form a , where 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
7)  1.5  1  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
28
35
3 3
2)
3 11

9
33
>
<
 
5 5
7 5
2 5
3)
2 8
25
35
1 11
3 11
10
16
5
3
4)
3 12
  
11
33
15
36
>
<

9 1
16 1
9
16
4 4
9 4

16
36
Graph the fractions below on a number line, then
order them from least to greatest.
7 3
1 1
, ,  ,
5 5
3 9
1

3
1
1
2
1

1
2
1
9
0
3
5
1
2
1 1 3 7
 , , ,
3 9 5 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
2
-2
5
3
-1
0
1
1 0.4
2
0.4
1
3.21
2
5
3
3
3.21
4
4
Which is greater 0.58 or ?
7
0 571 4285 7
4
0.58
7 4.0000000
7
35
40
35
50
50
49
0.58 > 0.571428
49
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.
11
0 16 8
1
32
1
64
1
4
1
2
1