Rational number
Elementary
A rational number is a number that can be written as a fraction of whole numbers, or the negative of one.
High school
A rational number is a number that can be written as $p/q$, where $p$ and $q$ are integers and $q \neq 0$.
Undergraduate
A rational number is an element of $\mathbb{Q}$, constructed as equivalence classes of pairs $(p, q)$ of integers with $q \neq 0$, where $(p, q) \sim (r, s)$ if $p s = q r$.
Properties
- A real number is rational if and only if its decimal expansion either ends or repeats.
- Between any two real numbers there is a rational number: $\mathbb{Q}$ is dense in $\reals$.