Pi is a number.
Decimal representation . A decimal representation of a non-negative real number r is an expression in the form of a series , traditionally written as a sum A mathematical constant is a special number , usually a real number , that is `` significantly interesting in some way '' . Number theory or , in older usage , arithmetic is a branch of pure mathematics devoted primarily to the study of the integers . Pi . Being an irrational number , can not be expressed exactly as a fraction ( equivalently , its decimal representation never ends and never settles into a permanent repeating pattern ) . In more modern mathematical analysis , the number is instead defined using the spectral properties of the real number system , as an eigenvalue or a period , without any reference to geometry .