We propose to use a simple inductive type as a basis to represent the field of rational numbers. We describe the relation between this representation of numbers and the representation as fractions of non-zero natural numbers. The usual operations of comparison, multiplication, and addition are then defined in a naive way. The whole construction is used to build a model of the set of rational numbers as an ordered archimedian field. All constructions have been modeled and verified in the Coq proof assistant.