Real Numbers & Decimal Expansions
- Rational Numbers ($\mathbb{Q}$): Terminating or non-terminating repeating (recurring) decimals.
- Irrational Numbers: Non-terminating and non-repeating decimals ($\sqrt{2}, \sqrt{3}, \pi$).
- Rationalising the Denominator:
$$\frac{1}{\sqrt{a} + \sqrt{b}} \times \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} - \sqrt{b}} = \frac{\sqrt{a} - \sqrt{b}}{a - b}$$
