Download Classifying Numbers - Renton School District

CLASSIFYING NUMBERS
8th grade Math – Number Systems Unit
Number Types




Whole
Integers
Rational Numbers
Irrational Numbers
 Which
is which?
 How can you tell them apart?
Whole Numbers

The Counting Numbers including 0.
 Ex:
0,1,2,3,4,5……
Integers

Positive and negative whole numbers.
 -3,-2,-1,0,1,2,3…….
 How
are integers and whole numbers related?
19
Whole Numbers = Integers

All whole numbers are integers because integers
include both positive and negative whole numbers.
Integers
Whole
Numbers
Rational Numbers



Numbers that can be written as a fraction a/b.
Numbers that are terminating decimals.
Numbers that are repeating decimals.
 4.375
 2.5
=
 0.3
=
 How
=4
5
2
10
3 1
=
9 3
375
1000
= 2
= 4
1
2
3
8
do rational numbers relate?
Rational Numbers = Integers = Whole
Numbers

All rational numbers are integers and whole
numbers because you can make them into a fraction
as a value out of 1.

24
8 567 −76 24 −64
,− ,
,
,
,
1
1 1
1
3
8
Rational
Number
Integer
Whole
Irrational Numbers

Numbers that cannot be made into a simple
fraction; they have a decimal that keeps going and
going called non-terminating and non-repeating.
π
, √2 , 4.232332333…. , -√8
Are Irrational Numbers Related?

Irrational Numbers are by themselves because they
cannot be made into fractions, integers or whole
numbers.
Rational Number
Integer
Irrational
Numbers
Whole
Let’s Practice!

State which type of number these examples are:
Type of Number
• 0
• 47
24
•
8
56
1
•
• 279
Type of Number
•
•
•
•
•
2.454554555….
√6
π
-3.4224222….
-√10
Practice Continued

State which type of number these examples are:
Type of Number
•
•
•
•
•
-4
-√100
-12
81
9
√25
Type of Number
•
•
•
•
•
2.45
-0.6
34 ½
¾
-7.5
Answers
Whole
(Integer and Rational)
•
•
•
•
•
0
47
24/8
56/1
279
Integer
(Rational)
Irrational
•
•
•
•
•
2.454554555….
√6
π
-3.4224222….
-√10
•
•
•
•
•
-4
-√100
-12
-81/9
-√25
Rational
•
•
•
•
•
2.45
-0.6
34 ½
¾
-7.5
Quiz

Place these numbers into the correct category on the
chart to prove your understanding.
 -3,
27
,
3
π, 4.68, √13, -√49, 3.14144…, 8, ¼, 3.25,
61, 0.8, √144, -
30 244
,
,
5
2
and 0
Rational
Number
Integer
Irrational
Numbers
Whole
How did you do?
Rational
Number
¼
0.8
π
√13
Irrational
Numbers
3.14144…
3.25
4.68
-3
Integer
-√49
30
-5
8
244
2
27
3
Whole
0
61
√144
Explanation Time!

Explain with a chart how these types of numbers
are related and give examples of each:
 Whole
numbers
 Integers
 Rational Numbers
 Irrational Numbers
 Which
is which?
 How can you tell them apart?
The
counting
numbers.
0, 3, 5, 18,
53, 721,
8943
Irrational Number
Any + o r –
whole
number.
-712, -53,
-4/2, -√9,
Whole Number
Can be
made into a
fraction
a/b.
¼ , 4.25, 8,
-3, .7
repeating
Integer
Rational Number
Conclusion
Any number
that cannot be
made into a
fraction.
2.34344….,
√11, π