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