classifying numbers
DESCRIPTION
7. -√36. ¾. π. Classifying Numbers. 2.12122…. 0. 8 th 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……. 9. 43. 12. - PowerPoint PPT PresentationTRANSCRIPT
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CLASSIFYING NUMBERS
8th grade Math – Numeration Unit
7π
-√36 ¾
02.12122….
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Number Types
Whole Integers Rational Numbers Irrational Numbers
Which is which? How can you tell them apart?
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Whole Numbers
The Counting Numbers including 0. Ex: 0,1,2,3,4,5……
235
9
12101
43
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Integers
Positive and negative whole numbers. -3,-2,-1,0,1,2,3…….
How are integers and whole numbers related?
-2719
-132
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Whole Numbers = Integers
All whole numbers are integers because integers include both positive and negative whole numbers.
Integers
Whole Numbers
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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?
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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, -64/8Rational
Number
Integer
Whole
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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
Pi Pi
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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
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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
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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
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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
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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
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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
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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?
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ConclusionR
ati
onal
Num
berCan be
made into a fraction a/b.¼ , 4.25, 8, -3, .7 repeating
Inte
ger Any + o r
– whole number.-712, -53, -4/2, -√9,
Whole
N
um
berThe
counting numbers.0, 3, 5, 18, 53, 721, 8943
Irra
tional
Num
berAny
number that cannot be made into a fraction.2.34344…., √11, π
Remember: All
whole #’s are
integers and all
integers and whole
#’s are rational #’s
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References
http://www.examiner.com/math-education-in-dallas/history-of-pi Pi picture
Microsoft PowerPoint SmartArt Graphic organizers