Rational versus Irrational

Rational numbers are numbers that can be written as a fraction.

Irrational numbers are numbers that cannot be written as a fraction. Remember, something like $\frac{\pi}{3}$ is not a fraction because the numerator in this case is not an integer.

Where do these terms come from?

Another way to say fraction is of course "ratio." So rational numbers are ones that can be written as a "ratio." Irrational numbers are ones that cannot be written as a "ratio". Get it? Pretty cool!