8th grade Math – Number Systems Unit 7 -√36 ¾ π Classifying Numbers 2.12122…. 8th grade Math – Number Systems Unit

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

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

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

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

Rational Numbers Numbers that can be written as a fraction a/b. Numbers that are terminating decimals. Numbers that are repeating decimals. 4.375 = 4 375 1000 = 4 3 8 2.5 = 2 5 10 = 2 1 2 0. 3 = 3 9 = 1 3 How do rational numbers relate?

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 , 567 1 , −76 1 , 24 3 , −64 8 Rational Number Integer Whole

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 , 4.232332333…. , -√8

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

Let’s Practice! State which type of number these examples are: 47 24 8 56 1 279 Type of Number 2.454554555…. √6 π -3.4224222…. -√10

Practice Continued State which type of number these examples are: -4 -√100 -12 - 81 9 √25 Type of Number 2.45 -0. 6 34 ½ ¾ -7.5

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

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, 0. 8 , √144, - 30 5 , 244 2 , and 0 Rational Number Integer Whole Irrational Numbers

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

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?

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. 2.34344…., √11, π