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.
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
Natural numbers are counting numbers starting at 1.
Examples:

8 
2 
It can be simplified to 8 ÷ 2 = 4.
This is just 5.
Nonexamples:
It cannot be less than 1.
REMINDER: Counting numbers start at 1 and add 1 each time.
Whole Numbers
Whole numbers are natural numbers together with 0.
Examples:
Keep going in this direction counting up by 1.

0 
4 
This is just the same as 0.
A whole number greater than 0.
Nonexamples:
These are not whole numbers.
Integers
Integers are all whole numbers and their opposites (negatives), as well as 0.
Examples:
Rational
Rational is 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.
Examples:

2  2  =    8 
3  3 

6  =  6 
1 

0.333  =  1 
3 
Nonexample:
This is NOT rational because it cannot be written as a simple fraction.
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 the types of numbers above it as well.
Example: Integers are not only integers but are whole and natural numbers as well.
Irrational Numbers
Irrational numbers are all numbers that cannot be written as a simple fraction; they are written as nonrepeating, nonterminating decimals.
Examples:
This is equal to 3.14159265359...
This is equal to 1.4142135....
NOTE: If a number in a square root is not a perfect square, it is most likely irrational.
Look at the diagram above.
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 makeup one type of number: real numbers.
Real Numbers
Real numbers are any and all numbers you can find on a number line.
Examples:
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:
It is time to try your hand at some problems to see how well you can classify numbers.
We help prepare learners for a future that cannot yet be defined. They must be ready for change, willing to learn and able to think critically. Elephango is designed to create lifelong learners who are ready for that rapidly changing future.