What Is the Difference Between A Rational Number and An Irrational Number?

Learn to tell the difference between rational and irrational numbers.

Jason Marshall, PhD,
September 21, 2011


Rational numbers are all the numbers that can be written like fractions with one integer (the numerator) over another integer (the denominator). This includes all the normal fractions that you’re familiar with—such as 1/2, 3/7, and so on—as well as all the integers. Why the integers? Because they can be written like fractions too. For example, the integer 5 can also be written 5/1. Irrational numbers, on the other hand, are all the numbers that cannot be written this way.
For more, see What are Rational Numbers?