CLASSIFYING NUMBERS

8th grade Math – Numeration Unit

7π

-√36 ¾

02.12122….

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……

235

9

12101

43

Integers

Positive and negative whole numbers. -3,-2,-1,0,1,2,3…….

How are integers and whole numbers related?

-2719

-132

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 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, -64/8Rational

Number

Integer

Whole

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

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

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

• 2.45• -.6 repeating• 34 ½• ¾• -7.5

Type of Number

• -4• -√100• -12• -81/9• -√25

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

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

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

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?

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

References

http://www.examiner.com/math-education-in-dallas/history-of-pi Pi picture

Microsoft PowerPoint SmartArt Graphic organizers