1. Real Numbers ($\mathbb{R}$)

Everything you study in Class 9 falls under Real Numbers. These are divided into two distinct groups that do not overlap:

• Rational Numbers ($\mathbb{Q}$): Any number that can be written as $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

  • Examples: $\frac{2}{3}, -5, 0, 1.5, 0.333...$

• Irrational Numbers: Numbers that cannot be written as a simple fraction. Their decimal expansions are non-terminating and non-recurring.

  • Examples: $\sqrt{2}, \sqrt{3}, \pi, 0.101101110...$

2. Breakdown of Rational Numbers

Rational numbers are further split into smaller, more specific groups:

• Integers ($\mathbb{Z}$): The complete set of negative and positive whole numbers.

  • $\{..., -3, -2, -1, 0, 1, 2, 3, ...\}$

• Whole Numbers ($W$): Starting from zero.

  • $\{0, 1, 2, 3, ...\}$

• Natural Numbers ($\mathbb{N}$): Also called "Counting Numbers."

  • $\{1, 2, 3, ...\}$