Pi is a real number, as all numbers that exist on a number line are real. Real numbers include all rational and irrational numbers; pi is defined as an irrational number.
There are several categories that refer to types of numbers. Numbers that aren't real numbers include imaginary and complex numbers. Imaginary numbers are all numbers that are divisible by i, or the square root of negative one.
Rational numbers are those that can be written as a simple fraction. Therefore, 0.11111... (repeating) is a rational number because it can be written as 1/9, but pi is not a rational number because there is no fraction that is equal to the number pi.