Why is 3.14 rational, but pi is not?

Because pi is a non terminating number which means it repeats but not the same numbers one after another

3.14 is rational because it's just an approximation of pi. 3.14 can be written as the fraction 3.14/100 but pi is never ending and cannot be written as a fraction since it goes on forever. (To be a rational number, the number has to be able to be written as a fraction.)