Number Systems in Class 9 Math
1. Overview of Number Systems
One method of representing numbers is using a number system. Different kinds of numbers have
various uses in mathematics.
2. Number Types
(a) Natural Numbers (N)
* Counting from 1. * Examples: 1, 2, 3, 4, 5,... One is the smallest natural number.
(b) Whole Numbers (W)
* All natural numbers, including zero For instance, 0, 1, 2, 3, 4,
* 0 is the smallest whole number.
(c) Z (integers)
* Both whole and negative numbers For instance: -3, -2, -1, 0, 1, 2, 3,
(d) Rational Quantities (Q)
* Quantities that can be written as p/q, where:
* q ≠ 0 * p and q are integers * Examples: 1/2, -3/5, 4, 0.75
* Recurring decimal expansion might be either non-terminating or terminating.
(e) Irrational Numbers
* Numbers that don't fit into the p/q format Decimal expansion is neither repeating nor terminating.
Examples are √2, √3, and π.
(f) Actual Numbers (R)
* Real numbers are made up of all rational and irrational numbers combined. A real number is
represented by each point on the number line.
3. Real Number Representation on a Number
Line
1. Overview of Number Systems
One method of representing numbers is using a number system. Different kinds of numbers have
various uses in mathematics.
2. Number Types
(a) Natural Numbers (N)
* Counting from 1. * Examples: 1, 2, 3, 4, 5,... One is the smallest natural number.
(b) Whole Numbers (W)
* All natural numbers, including zero For instance, 0, 1, 2, 3, 4,
* 0 is the smallest whole number.
(c) Z (integers)
* Both whole and negative numbers For instance: -3, -2, -1, 0, 1, 2, 3,
(d) Rational Quantities (Q)
* Quantities that can be written as p/q, where:
* q ≠ 0 * p and q are integers * Examples: 1/2, -3/5, 4, 0.75
* Recurring decimal expansion might be either non-terminating or terminating.
(e) Irrational Numbers
* Numbers that don't fit into the p/q format Decimal expansion is neither repeating nor terminating.
Examples are √2, √3, and π.
(f) Actual Numbers (R)
* Real numbers are made up of all rational and irrational numbers combined. A real number is
represented by each point on the number line.
3. Real Number Representation on a Number
Line
