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CLASSIFYING NUMBERS 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 The Counting Numbers including 0. Ex: 0,1,2,3,4,5…… Integers Positive and negative whole numbers. -3,-2,-1,0,1,2,3……. How are integers and whole numbers related? 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 2.5 = 0.3 = How =4 5 2 10 3 1 = 9 3 375 1000 = 2 = 4 1 2 3 8 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 8 567 −76 24 −64 ,− , , , , 1 1 1 1 3 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 Integer Irrational Numbers Whole 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 Practice Continued State which type of number these examples are: Type of Number • • • • • -4 -√100 -12 81 9 √25 Type of Number • • • • • 2.45 -0.6 34 ½ ¾ -7.5 Answers Whole (Integer and Rational) • • • • • 0 47 24/8 56/1 279 Integer (Rational) Irrational • • • • • 2.454554555…. √6 π -3.4224222…. -√10 • • • • • -4 -√100 -12 -81/9 -√25 Rational • • • • • 2.45 -0.6 34 ½ ¾ -7.5 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, - 30 244 , , 5 2 and 0 Rational Number Integer Irrational Numbers Whole How did you do? Rational Number ¼ 0.8 π √13 Irrational Numbers 3.14144… 3.25 4.68 -3 Integer -√49 30 -5 8 244 2 27 3 Whole 0 61 √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? The counting numbers. 0, 3, 5, 18, 53, 721, 8943 Irrational Number Any + o r – whole number. -712, -53, -4/2, -√9, Whole Number Can be made into a fraction a/b. ¼ , 4.25, 8, -3, .7 repeating Integer Rational Number Conclusion Any number that cannot be made into a fraction. 2.34344…., √11, π