Objective - To classify and identify numbers within the real number system.

Understanding Rational and Irrational
“Makes Sense” “Doesn’t Make Sense”
Rational Numbers
-Any number that can be written as a fraction.
fractions wholes integers terminating decimals
2

3
7
18
 7

1

18
1
0.49
 49
100 repeating decimals
0.7
 7
9
Irrational Numbers
-Non-terminating and non-repeating decimals.
-can’t be written as a fraction.
3

1.73205...
1.212112111211112...
0.123456789101112...
0.15255355545555...

Sets of Numbers
Naturals - Natural counting numbers.
{ 1, 2, 3… }
Wholes - Natural counting numbers and zero.
{ 0, 1, 2, 3… }
Integers - Positive or negative natural numbers or zero.
{ … -3, -2, -1, 0, 1, 2, 3… }
Rationals - Any number which can be written as a fraction.
Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal.
Reals - Rationals and irrationals.

Sets of Numbers
Reals
2
3
Rationals
, 7, -0
.
4
- any number that can be written as a fraction.
Irrationals
2
- non-terminating and non-repeating decimals
Fractions/Decimals
1
6
4
Integers
, -0
.
32, - 2
.
1
…
-3, -2, -1, 0, 1, 2, 3
...
Negative Integers
…
-3, -2, -1
Zero
0
Wholes
0, 1, 2, 3
...
Naturals
1, 2, 3
...

Sets of Numbers
This is a Venn Diagram that displays the following sets of numbers:
Naturals, Wholes, Integers, Rationals, Irrationals, and Reals.
Reals
2
3
-3
Rationals
Integers
-19
-2
.
65
Wholes
0
6
1
4
Naturals
1, 2, 3
...
Irrationals
2

Identify each number below as natural, whole, integer, rational, irrational, or real. More than one may apply.
1)
7
8
Rational , Real
2) 0 Whole, Integer, Rational , Real
3)

24 Integer, Rational , Real
4) 6 Irrational , Real
5) 8 Natural ,Whole, Integer, Rational , Real

Identify each number below as natural, whole, integer, rational, irrational, or real. More than one may apply.
6)
 4
5
Rational , Real
7)

9 Integer, Rational , Real
8) 16
9)

25
Natural ,Whole, Integer, Rational , Real
Integer, Rational , Real
10) 8 Irrational , Real

• (Hint: turn them all into decimals)

2 1
, , 8,
3 5
10
3

0.6, 0.2, 2.9, 3.3
-1
0 1 2 3 4 5 6

8

8,

4,
5
2
,

3.75

5
2

-4 -3 -2 -1 0 1 2 3 4 5 6 7

4,

3.75,
5
2
, 8

• Turn them both either to:
– Fractions and use the heart method
– Decimals and compare place values

Use < , > , or = to compare.
1)
4
0.6
9
=
2
3

0.6
0.6

0.6
3) 0.5
9
>
5

5
9 10
2) 0.65
8
<
0.625

0.65
4)
3
10
<
1
3

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