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

**Related Pages**

More Lessons for Grade 9

Math Worksheets

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

Numbers you count on your hands and your feet

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.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.