Classify Real Numbers

In this middle school math tutorial, we will define and classify real numbers.

Real Numbers are a set of numbers that include values considered to be rational and irrational. The rational numbers can be subdivided into the classifications of rational numbers, integers, whole numbers, and natural numbers.

All the numbers students work within most math classes up to Algebra are usually real numbers. Students should have a firm understanding of the various types of real numbers by the time they complete the 8th grade and before they start Algebra.

Here is a breakdown of the Real Number classifications with examples. A short tutorial video is included at the end of this post with some supplementary material.

Rational Numbers

A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers, however, the denominator cannot be zero (0). The denominator must be 1 or higher. Rational numbers can, also, ne expressed as terminating or repeating decimals. Rational numbers include all integers, whole numbers, and natural or counting numbers as well. Any real number that is determined not to be rational is classified as irrational.

Examples of rational numbers include the following: 1.75 7/4 .001 1/100 .25 1/2 .666 3/4


Integers are another subcategory of real numbers. Integers are rational numbers as well. The word “integer” is from Latin meaning “whole.” Integers include the number zero, all whole numbers, and their opposites. Integers include all whole and natural numbers. Integers do not include fractions or decimals.

Examples of integers include the following: -25 -3 -1 0 17 25

Whole Numbers

Whole numbers are all natural numbers and zero. They are classified as real numbers, rational numbers, and integers.

Examples of whole numbers include the following: 0 1 2 3 4 5 ….

Natural Numbers

Natural numbers are often called counting numbers. They are used for counting and ordering They are the most basic numbers.

Examples of natural numbers include the following: 1 2 3 4 5 ….

Irrational Numbers

Irrational numbers are real numbers that are not rational. When in decimal form, an irrational number will never repeat or terminate. They are called non-terminating continued fractions. The most used irrational number for middle school students is pi. Other examples of irrational numbers include the square roots of numbers that are not perfect squares.

Examples of irrational numbers include the following:

Video Tutorial

The chart shared in the video can be found here.


Interactive Classes

For an interactive middle school math class on this material, click here.


Check out the inactive lesson series (4 lessons) on Real Numbers.

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