7 36 CLASSIFYING NUMBERS 0 2 12 122

7 π -√ 36 ¾ CLASSIFYING NUMBERS 0 2. 12 122 …. 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 43 235 101 12

Integers Positive and negative whole numbers. � -3, -2, -1, 0, 1, 2, 3……. � How -27 are integers and whole numbers related? -132 19

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

Rational 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?

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

Irrational 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

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. 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 -. 6 repeating 34 ½ ¾ -7. 5

Answers Irrational Whole • • • 0 47 24/8 56/1 279 • • • 2. 454554555…. √ 6 π -3. 4224222…. -√ 10 Integer • • • -4 -√ 100 -12 -81/9 -√ 25 Rational • 2. 45 • -. 6 repeating • 34 ½ • ¾ • -7. 5

Quiz Place these numbers into the correct category on the chart to prove your understanding. 27/3, π, 4. 68, √ 13, -√ 49, 3. 14144…, 8, ¼, 3. 25, 61, . 8 repeating, √ 144, -30/5, 244/2, 0 � -3, Rational Number Integer Irrational Numbers Whole

How did you do? Rational Number ¼ . 8 repeating π √ 13 Irrational Numbers 3. 25 4. 68 -3 Integer -√ 49 -30/5 27/3 3. 14144… 8 244/2 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 Any number that cannot be made into a fraction. 2. 34344…. , √ 11, π Irrational Number Any + o r – whole number. -712, -53, -4/2, -√ 9, hole w l l A : ber m e s and R r e g e t in #’s are s and whole ger all inte rational #’s are Whole Number Rational Number Can be made into a fraction a/b. ¼ , 4. 25, 8, -3, . 7 repeating Integer Conclusion

References http: //www. examiner. com/math-education-indallas/history-of-pi � Pi picture Microsoft Power. Point Smart. Art � Graphic organizers