# The Real Number System

In these lessons, we learn the real number system and the different types of real numbers.

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The following diagram shows the real number system and how real numbers can be classified. Scroll down the page for more examples and solutions on classifying real numbers.

How to classify real numbers?

Classifying Real Numbers
This video explains the different classifications of Real Numbers and has a number of examples.

Ordering and Classifying Real Numbers

Classifying Real Numbers
Defines the different subsets of Real Numbers we regularly work with and how to classify them using a Venn Diagram.

Number Types (Math Song)
Natural numbers are naturally
1, 2, 3, 4, 5, 6, and so on

Whole numbers are natural numbers plus zero
That’s the only difference, oh, oh
0, 1, 2, 3, and so on

Integers are whole numbers plus negatives
They look a little bit like this
-2, -1, 0, 1, and so on

Last but not least, not to be outdone
Rational numbers are integers plus fractions
Like -3, 1/2, 5/8 and 14.2

All natural numbers are whole numbers
All whole numbers are integers
All integers are rational numbers
Now listen to that drummer!

What about 4? It’s a natural number so it’s also whole, integer, and rational
What about -2? Integer and rational
What about 1.5? It’s just rational
What about 0? It’s whole, integer, and rational

All natural numbers are whole numbers
All whole numbers are integers
All integers are rational numbers
Now listen to that drummer!

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.