How to Recognize Rational Numbers

How can you tell when a number is rational? Is 31/37 rational? Is the square root of 15 rational? HOW DO YOU KNOW?

To start off, a rational numbers means a number that is able to be displayed as a fraction. For example, the number 0.837837837837837837837837… might not look like it would be able to be displayed as a fraction, but it actually is! Surprisingly, that number is 31/37 in decimal form! Now, if you ask yourself the questions below, you will always be able to tell whether a number is rational or not.


  1. Is the number a whole number?
  2. Is the number a fraction?
  3. Is the number a repeating decimal?
  4. If the number is being square rooted, is it a perfect square?

If the answer to one of these questions is yes, then the number is rational.

What are some examples of irrational numbers? π, or Pi, is an irrational number, as it does not follow any of the rules above.  The number π is 3.141592653589793238462643383279502884197169399375105820974… and goes on and on forever, never repeating.

Knowing the difference between rational and irrational numbers is important, and you should pay attention to what type of number you are using when making calculations! For example, when finding the area of a circle, you could leave your answer as 30π, or calculate 30 * 3.14, which equals 94.2 . While 30π is more accurate, 94.2 gives you a better idea of what this figure is actually close to.

These questions will help you classify any number as rational or irrational, and aid you in math class and beyond. Good luck, and make sure to think rationally.

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