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# Classifying numbers

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### Classifying numbers

1. 1. CLASSIFYING NUMBERS 8th grade Math – Numeration Unit
2. 2. Number Types  Whole  Integers  Rational Numbers  Irrational Numbers  Which is which?  How can you tell them apart?
3. 3. Whole Numbers  The Counting Numbers including 0.  Ex: 0,1,2,3,4,5……
4. 4. Integers  Positive and negative whole numbers.  -3,-2,-1,0,1,2,3…….  How are integers and whole numbers related? 19
5. 5. Whole Numbers = Integers  All whole numbers are integers because integers include both positive and negative whole numbers. Integers Whole Numbers
6. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 17. References  http://www.examiner.com/math-education-in- dallas/history-of-pi  Pi picture  Microsoft PowerPoint SmartArt  Graphic organizers