CBSE Class 9 Mathematics – Chapter 1: Number
Systems (Study Material)
A number system is a way of representing numbers using digits or symbols. Examples of numbers
include natural numbers, integers, fractions, decimals, and irrational numbers.
1. Natural Numbers (N)
• Counting numbers starting from 1.
• Examples: 1, 2, 3, 4, 5, ...
2. Whole Numbers (W)
• Natural numbers including zero.
• Examples: 0, 1, 2, 3, 4, ...
3. Integers (Z)
• Includes negative numbers, zero, and positive numbers.
• Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q)
• Numbers that can be written in the form p/q where p and q are integers and q ≠ 0.
• Examples: 1/2, -3/5, 4, 0.75
5. Irrational Numbers
• Numbers that cannot be written in p/q form.
• Their decimal form is non■terminating and non■repeating.
• Examples: √2, √3, π
6. Real Numbers
• All rational and irrational numbers together are called real numbers.
7. Decimal Expansion of Rational Numbers
• Rational numbers have either terminating decimals (Example: 1/2 = 0.5)
• or non■terminating recurring decimals (Example: 1/3 = 0.333...).
8. Laws of Exponents
• a^m × a^n = a^(m+n)
• a^m / a^n = a^(m−n)
Systems (Study Material)
A number system is a way of representing numbers using digits or symbols. Examples of numbers
include natural numbers, integers, fractions, decimals, and irrational numbers.
1. Natural Numbers (N)
• Counting numbers starting from 1.
• Examples: 1, 2, 3, 4, 5, ...
2. Whole Numbers (W)
• Natural numbers including zero.
• Examples: 0, 1, 2, 3, 4, ...
3. Integers (Z)
• Includes negative numbers, zero, and positive numbers.
• Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q)
• Numbers that can be written in the form p/q where p and q are integers and q ≠ 0.
• Examples: 1/2, -3/5, 4, 0.75
5. Irrational Numbers
• Numbers that cannot be written in p/q form.
• Their decimal form is non■terminating and non■repeating.
• Examples: √2, √3, π
6. Real Numbers
• All rational and irrational numbers together are called real numbers.
7. Decimal Expansion of Rational Numbers
• Rational numbers have either terminating decimals (Example: 1/2 = 0.5)
• or non■terminating recurring decimals (Example: 1/3 = 0.333...).
8. Laws of Exponents
• a^m × a^n = a^(m+n)
• a^m / a^n = a^(m−n)
