Contributor: Briana Pincherri. Lesson ID: 11341
A number is a number, right? NATURALly, there is a WHOLE number of types of numbers you need to know to be able to RATIONALly deal with more than a FRACTION of math problems. Learn with online help!
It is time for your secret detective classification skills to come out! This lesson needs help in determining what type of number a number truly is. Are you up to the challenge?
While you may think of a number as just a plain old number, it is so much more.
Numbers are classified into different types of numbers based on various things like:
In this lesson, you will see how to classify numbers. Let's get started by looking at some different types of numbers. Grab your math notebook to write this information down. It will help you keep things straight moving forward, especially when asked to classify numbers later.
Types of Numbers
Natural Numbers Counting numbers starting at 1
Examples 
1, 2, 3, 4, 5, …. 

8/2 
Can be simplified to 8 ÷ 2 = 4 

5.0 
This is just 5. 

NonExamples 
0, 10 
Cannot be less than 1 
REMINDER: Counting numbers start at 1 and add 1 each time.
Whole Numbers Natural numbers together with 0
Examples 
0, 1, 2, 3, 4,…. 
Keep going in this direction counting up by 1 
0/4 
This is just the same as 0 

101 
Whole number greater than 0 

Nonexamples 
½, .44 
These are not whole numbers 
Integers All whole numbers and their opposites (negatives), as well as 0
Examples: ..., 3, 2, 1, 0, 1, 2, 3, ...
Rational A number that can be written as a simple fraction a/b, where a and b are integers and b does not equal 0 (0 CANNOT be in the denominator). NOTE: This includes terminating and repeating decimals.
Terminating: When you divide the fraction there is a stop, it does not keep going. Ex. ½ = 0.5
Repeating: When you divide the fraction, the decimal repeats itself. Ex. 1/3 = 0.3333....
Examples:
Nonexample:
Each number discussed so far is a part of the next type of number. Here is a diagram to show this:
From this diagram, you can see that each type of number includes the type or types of number above it as well. Ex. Integers are not only integers, but are whole and natural numbers as well.
But wait a minute, what happens with fractions that, when divided, either do not terminate (stop) or do not repeat?
Irrational Numbers All numbers that cannot be written as a simple fraction; they are written as nonrepeating, nonterminating decimals.
Examples:
NOTE: If a number in a square root is not a perfect square, it is most likely irrational.
Look at the diagram above. Where could we add irrationals? They do not have anything in common with any other number listed to this point, so you must make them a completely separate category.
You may have noticed, all the number types talked about to this point make up one type of number: Real Numbers.
Real Numbers Any and all numbers you can find on a number line.
Examples: All numbers listed to this point are real numbers. This is because all natural numbers, whole numbers, integers, rational numbers, and irrational numbers, are real numbers.
Please take a minute to review the info just covered in the following video, then try the four problems at the end. Watch this video, Identifying Types of Real Numbers by Sharon Serano:
Is this all starting to make sense? It is time to try your hand at some problems to see how well you can classify numbers.
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