CLASSIFYING NUMBERS
8th grade Math – Numeration 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 have terminating decimals.
Numbers that have repeating decimals.
 4.375
= 4 375/1000 = 4 3/8
 2.5 = 2 5/10 = 2 1/2
 0.3 repeating = 3/9 = 1/3
 How
do rational numbers relate?
Rational Numbers = Integers = Whole
Numbers

All rational numbers are integers and whole
numbers because you can make them into a ratio (or
fraction) by putting a 1 under it.
 24/1,
-8/1, 567/1, -76/1, 24/3, -64/8
Rational
Number
Integer
Whole
Irrational Numbers

Numbers that cannot be made into a simple
fraction; they have a decimal that keeps going and
going.
π
, √2 , 4.23233…. , -√8
Are Irrational Numbers Related?

Irrational Numbers are by themselves because they
cannot be made into fractions (rational numbers) or
cannot be a positive or negative whole number
since there is no decimal.
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
-.6 repeating
34 ½
¾
-7.5
Answers
Irrational
Whole
•
•
•
•
•
0
47
24/8
56/1
279
•
•
•
•
•
2.454554555….
√6
π
-3.4224222….
-√10
Integer
•
•
•
•
•
-4
-√100
-12
-81/9
-√25
Rational
• 2.45
• -.6
repeating
• 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, .8 repeating, √144, -30/5, 244/2, 0
Rational
Number
Integer
Irrational
Numbers
Whole
How did you do?
Rational
Number
¼
.8 repeating
π
√13
Irrational
Numbers
3.25
4.68
-3
Integer
-√49
-30/5
27/3
3.14144…
8
244/2
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
References

http://www.examiner.com/math-education-indallas/history-of-pi
 Pi

picture
Microsoft PowerPoint SmartArt
 Graphic
organizers