Rational vs. Irrational Numbers

Identifying Rational and Irrational Numbers

​8.NSO.1. Define the real number system as composed of rational and irrational numbers.
a. Explain that every number has a decimal expansion, for rational numbers, the decimal

expansion repeats or terminates.

b. Convert a decimal expansion that repeats into a rational number.

What are rational and irrational numbers and how can we determine the difference between the two>

​

Essential Question:

As a reminder, the real number system, as seen below is what we use to categorize numbers by their characteristics.

Real Number System

In previous grade levels, you have used, almost exclusively, rational numbers.

Multiple Select

Preview Question:

Which categories does number -16 belong to according to its characteristics? Select all that apply.

• NATURAL

• WHOLE

• INTEGER

• RATIONAL

Multiple Select

Preview Question:

Which categories does number $$\frac{1}{2}$$ belong to according to its characteristics? Select all that apply.

• NATURAL

• WHOLE

• INTEGER

• RATIONAL

Watch the short video to learn about or remind yourself what make a number a rational number.

What's a rational number anyway?

Rational numbers are numbers that can be written as ratios/fractions.
Therefore, rational numbers can be written in many forms, as you see in the picture.​

Rational Numbers

In previous grade levels, you learned about terminating and repeating decimals, which are rational.

These types of decimals are rational because they can be written as a ratio of two number, as you can see in the image.

So what about those irrational numbers?

Rational means Ratio

Irrational means NOT a Ratio


Watch the video to learn more!

​

What is an irrational number?

The word irrational means not-rational.

So irrational numbers cannot be written as a ratio/fraction.

What does irrational mean?

​Pi is typically the most well known example of an irrational number.

Categorize

Options (11)

-2

3.45

0

$$0.\overline{5}$$  

$$\sqrt[]{9}$$  

$$\pi$$  

3.14

$$\sqrt[]{8}$$  

1.24903857....

$$-\sqrt[]{6}$$  

$$\frac{6}{13}$$  

Using a Calculator, if needed, sort the following values as rational or irrational.

Rational Numbers

Irrational Numbers

Poll

Please rate your overall understanding of rational and irrational numbers by choosing one of the options below:

• I am confused and need to spend some more time learning about these topics.

• I understand some but not all of the information and need more help!

• I understand, but may need more information!

• I'm good to go and feel like I could explain this to someone else!