Rational and Irrational Numbers

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

An irrational number is a number that cannot be expressed as a simple fraction. It cannot be written as \( \frac{a}{b} \) where \( a \) and \( b \) are integers.

Irrational

Rational

\( \sqrt{2} \)

Rational

Rational

An example of a rational number is \( \frac{1}{2} \) or 0.75.

An example of an irrational number is \( \pi \) or \( \sqrt{3} \).

The decimal representation of a rational number either terminates (like 0.5) or repeats (like 0.̅̅3̅̅).