Rational numbers

A rational number is any number that can be written as a fraction of two integers.

By definition, all rational numbers are also real numbers.

Notation

The set of rational numbers is usually denoted by the symbol \mathbb{Q}:

\mathbb{Q} = \left\{ \frac{a}{b} \mid a, b \in \mathbb{Z}, b \neq 0 \right\}

Examples of rational numbers

• \frac{1}{2}
• -3 (can be written as \frac{-3}{1})
• 0 (can be written as \frac{0}{1})
• 4.75 (can be written as \frac{19}{4})
• -0.1 (can be written as \frac{-1}{10})
• 3.333\ldots (can be written as \frac{10}{3})
• 7 (can be written as \frac{7}{1})

Non-examples of rational numbers

• \sqrt{2} (irrational)
• \pi (irrational)
• e (irrational)
• i (not a real number)