Home > Math Topics > Irrational Numbers >

Rational and Irrational Numbers

HSN-RN.B.3
Answer Keys Here

Aligned To Common Core Standard:

High School Numbers - HSN-RN.B.3

What is the Difference Between Rational and Irrational Numbers? Are you often confused between rational and irrational numbers? Don't worry! We have put together a list of the differences between them. Rational Numbers - A number that can be expressed in a ratio of two values. They are expressed in fractions where the denominator is not equal to zero. They are known to include perfect squares.The decimal expansion of rational numbers is either finite or recurring. Irrational Numbers - Values that cannot be written as a ratio of two integers is known as an irrational number. They cannot be written in fractions. They include surds that are expressions that include a root symbol. Sureds are used to quantify precise values. The decimal expansion of irrational numbers is non-finite and non-recurring. These worksheets will help students learn to identify if a number should classified as a rational or irrational number.

Printable Worksheets And Lessons





Homework Sheets

Determine the classification of the value presented.

  • Homework 1 - A rational number is a number that can be written as a ratio. That means it can be written as a fraction.
  • Homework 2 - An irrational number can be written as a decimal, but not as a fraction.
  • Homework 3 - See if we can further simplify the number to make it completely rational.



Practice Worksheets

What does a farmer have to do with number classification? I wish I knew too.

  • Practice 1 - An irrational number can be written as a decimal, but not as a fraction. They are made up of non-repeating numbers and seem like a series of endless digits.
  • Practice 2 - A rational number is a number that can be written as a ratio. That means it can be written as a fraction. Both the numerator and denominator of the fraction are whole numbers.
  • Practice 3 - Are the numbers that are presented to you rational or irrational numbers?



Math Skill Quizzes

Find the final value and classify it all together.

  • Quiz 1 - See if you can further simplify the number to make it completely rational.
  • Quiz 2 - If the number terminate it is therefore a rational number.
  • Quiz 3 - Start by stating what you know about rational and irrational numbers.


Why Do We Care About Irrational Numbers?

We learn many different things in math that we do not understand the importance. I cannot think of a single topic, except maybe the power of i, that sees this level of criticism by students greater than irrational numbers and values. We lay the foundation of this concept is most high school math classes, but you really will not understand the significance of it until you actually apply it in science class. These imaginary values are used to model physical and theoretical phenomena. We are all comfortable with your standard numbers line, where each successive follow in all directions differs by a fixed unit. When following this pattern, you can always find a rational value for a previous value. For every day scientific experiments this does not hold true due to the theory of chaos and all the possible variables. Take for example my asphalt driveway. Asphalt is a substance that contracts when cool and expands when hot. Do you think that the exact precise measure of length of my driveway differs between the winter and summer months? You can surely bet it does. In fact, I have measured it to have a 2.4 inches in length difference between the months of August and January. Using imaginary numbers, we can model this value and make sense of it.