What Type of Number Is It? (Classifying Numbers)

Lesson Plan - Get It!

Audio:

•  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:

• Is it positive or negative?
• Is it a fraction or a decimal?
• Do they repeat?

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:

• 1, 2, 3, 4, 5, ......

It can be simplified to 8 ÷ 2 = 4.

• 5.0

This is just 5.

Non-examples:

• 0, -10

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:

• 0, 1, 2, 3, 4, ...

Keep going in this direction counting up by 1.

This is just the same as 0.

• 101

A whole number greater than 0.

Non-examples:

• ½, 0.44

These are not whole numbers.

Integers

Integers are all whole numbers and their opposites (negatives), as well as 0.

Examples:

• ..., -3, -2, -1, 0, 1, 2, 3, ...

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.

• Terminating: When you divide the fraction there is a stop, it does not keep going.
  • Example: ½ = 0.5
• Repeating: When you divide the fraction, the decimal repeats itself.
  • Example: 1/3 = 0.3333....

Examples:

Non-example:

• 0.1234567...

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.

• What happens with fractions that, when divided, either do not terminate (stop) or do not repeat?

Irrational Numbers

Irrational numbers are all numbers that cannot be written as a simple fraction; they are written as non-repeating, non-terminating decimals.

Examples:

• π

This is equal to 3.14159265359...

• √2

This is equal to 1.4142135....

• 123.4587621356

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 makeup one type of number: real numbers.

Real Numbers

Real numbers are 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.

• All examples to this point are examples of real numbers because they can all be found on a numberline.

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.