Pi is not a rational number. It is considered irrational. A rational number is able to be written as a fraction with integers for both the numerator and denominator.
In some rational numbers, when the numerator is divided by the denominator, the result has a decimal component that repeats. For instance, 2/3 is a rational number that is also written 0.666..., which indicates the infinite repetition. However, pi never repeats.
Archimedes, a mathematician from ancient Greece, calculated pi to between 3.141 and 3.143. By 1400, mathematicians in India had traced pi to 11 digits. As of 2013, pi has been calculated to 10 trillion digits with no repetition. Pi is often written as 3.14 or 22/7, but these are just approximations.