1. 8th grade Math – Number Systems Unit7
-√36 π
Classifying Numbers ….
8th grade Math – Number Systems Unit

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

3. Whole Numbers 9 43 12 101 235 The Counting Numbers including 0.
Ex: 0,1,2,3,4,5…… 9 43 12
101
235

4. Integers -132 -27 19 Positive and negative whole numbers.
-3,-2,-1,0,1,2,3…….
How are integers and whole numbers related?
-132
-27 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 are terminating decimals.
Numbers that are repeating decimals.
= =
2.5 = =
0. 3 = = 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 fraction as a value out of 1.
24 1 , − 8 1 , , −76 1 , , −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 called non-terminating and non-repeating.
π , √2 , …. , -√8

9. Are Irrational Numbers Related?
Irrational Numbers are by themselves because they cannot be made into fractions, integers or whole numbers.
Rational Number
Irrational Numbers
Integer
Whole

10. Let’s Practice! State which type of number these examples are:47
24 8
56 1
279
Type of Number …. √6 π ….
-√10

11. Practice Continued State which type of number these examples are:-4
-√100
-12
√25
Type of Number
2.45
-0. 6
34 ½
-7.5

12. (Integer and Rational)
Answers
Rational
2.45
-0. 6
34 ½
-7.5
Integer
(Rational) -4
-√100
-12
-81/9
-√25
Whole
(Integer and Rational) 47
24/8
56/1
279
Irrational …. √6 π ….
-√10

13. Quiz
Place these numbers into the correct category on the chart to prove your understanding.
-3, , π, 4.68, √13, -√49, …, 8, ¼, 3.25, 61, , √144, , , and 0
Rational Number
Integer
Whole
Irrational Numbers

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

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 Can be made into a fraction a/b.
Remember: All whole #’s are integers and all integers and whole #’s are rational #’s
Conclusion
Rational Number
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,
Whole Number
The counting numbers.
0, 3, 5, 18, 53, 721, 8943
Irrational Number
Any number that cannot be made into a fraction.
…., √11, π