# Number System - Rational Number - $\mathbb{Q}$

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers

$$\frac{\displaystyle p}{\displaystyle q} = \frac{\displaystyle \text{p (numerator)}}{\displaystyle \text{q (non-zero denominator)}}$$

Since the non-zero denominator q may be equal to 1, every integer is a rational number.

Rational numbers are also known as:

• the rationals,
• the field of rationals
• or the field of rational numbers

The rational numbers together with addition and multiplication form field which contains the integers and is contained in any field containing the integers.

The set of rational numbers is countable.