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 Number theory or , in older usage , arithmetic is a branch of pure mathematics devoted primarily to the study of the integers . The number is a mathematical constant , the ratio of a circle 's circumference to its diameter , commonly approximated as 3.14159 . 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 the 20th and 21st centuries , mathematicians and computer scientists discovered new approaches that , when combined with increasing computational power , extended the decimal representation of to many trillions of digits after the decimal point .