‘π’ is

A real number is called RATIONAL when it can be written as p/q, where p and q are integers and q is not zero; a rational number's decimal expansion always terminates or repeats. A real number is IRRATIONAL when no such pair of integers exists, so its decimal expansion is non-terminating and non-repeating. Separately, a PRIME NUMBER is a narrower classification that applies only to integers greater than 1 having exactly two positive divisors, 1 and itself.

The constant π (≈ 3.14159...) has been mathematically proven to have a decimal expansion that never terminates and never settles into a repeating block, and no ratio of two integers reproduces its exact value. This is exactly the defining condition for an irrational number.

• An improper fraction and a proper fraction are both, by definition, ratios of two integers — so their decimal forms terminate or repeat, unlike π's expansion.

• The 'prime number' classification applies only to integers greater than 1 with exactly two divisors; π is not even an integer, so that definition cannot apply to it at all.

Hence, by the standard definition of rational and irrational numbers, π is classified as an irrational number.