Definition:Rational Number

Definition
A number in the form $\dfrac p q$, where both $p$ and $q$ are integers ($q$ non-zero), is called a rational number.

The set of all rational numbers is usually denoted $\Q$.

Thus:
 * $\Q = \left\{{\dfrac p q: p \in \Z, q \in \Z_{\ne 0}}\right\}$

A rational number is positive $p \cdot q > 0$. It is negative iff $p \cdot q < 0$ and it is zero  $p \cdot q = 0$. Every non-zero rational number is either positive or negative.

Also denoted as
Variants on $\Q$ are often seen, for example $\mathbf Q$ and $\mathcal Q$, or even just $Q$.

Also see

 * Definition:Irrational Number