This document provides an overview of different types of numbers: whole numbers, integers, rational numbers, and irrational numbers. It defines each type and provides examples. Whole numbers are the counting numbers including 0. Integers include both positive and negative whole numbers. Rational numbers can be written as fractions, while irrational numbers cannot be written as fractions and have non-repeating decimals. The document uses examples and diagrams to illustrate how the different number types are related and how to identify each one.

1. CLASSIFYING NUMBERS
8th grade Math – Numeration Unit

2. Number Types
 Whole
 Integers
 Rational Numbers
 Irrational Numbers
 Which is which?
 How can you tell them apart?

3. Whole Numbers
 The Counting Numbers including 0.
 Ex: 0,1,2,3,4,5……

4. Integers
 Positive and negative whole numbers.
 -3,-2,-1,0,1,2,3…….
 How are integers and whole numbers related?
19

5. Whole Numbers = Integers
 All whole numbers are integers because
integers include both positive and negative
whole numbers.
Integers
Whole
Numbers

6. 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?

7. 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

8. 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

9. 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.
Irrational
Numbers
Rational
Number
Integer
Whole

10. 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

11. Practice Continued
 State which type of number these examples
are:
Type of Number
• 2.45
• -.6 repeating
• 34 ½
• ¾
• -7.5
Type of Number
• -4
• -√100
• -12
• -81/9
• -√25

12. Answers
Whole
• 0
• 47
• 24/8
• 56/1
• 279
Irrational
• 2.454554555….
• √6
• π
• -3.4224222….
• -√10
Integer
• -4
• -√100
• -12
• -81/9
• -√25
Rational
• 2.45
• -.6
repeating
• 34 ½
• ¾
• -7.5

13. 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
Irrational
Numbers
Rational
Number
Integer
Whole

14. How did you do?
Rational
Number
Integer
Whole
Irrational
Numbers
-3
27/3
π
4.68√13
-√49
3.14144…
8
¼
3.25
61
.8 repeating
√144
-30/5
244/2
0

15. 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?

16. Conclusion
RationalNumber
Can be
made into
a fraction
a/b.
¼ , 4.25, 8,
-3, .7
repeating
Integer Any + o r –
whole
number.
-712, -53,
-4/2, -√9,
WholeNumber
The
counting
numbers.
0, 3, 5, 18,
53, 721,
8943
IrrationalNumber
Any number
that cannot be
made into a
fraction.
2.34344….,
√11, π

17. References
 http://www.examiner.com/math-education-in-
dallas/history-of-pi
 Pi picture
 Microsoft PowerPoint SmartArt
 Graphic organizers