## Number Systems

CBSE Class 9 Maths
Important Points To Remember

Counting numbers 1, 2, 3, 4... are called Natural Numbers (N)

Whole Numbers (W): Natural numbers 1, 2, 3... together with number 0 (zero) are called Whole Numbers

All natural numbers, zero and negative numbers together i.e. ...., –4, –3, –2, –1, 0, 1, 2, 3, 4, ... are known as Integers (Z).

Rational Numbers (Q): Numbers of the form p/q where p, q both are integers and q ≠ 0.

Every rational number have either terminating or repeating decimal representation.

The decimal expansion of an irrational number is non-terminating and non-repeating.

There are infinitely many rational numbers between any two given rational numbers.

Real numbers: It is a collection of both rational and irrational numbers.

All real numbers can be represented on a number line. Every point on the number line represents a unique real number.

For every given positive real number x, we can find √x geometrically.

If r is a rational number and s is an irrational number, then

r + s is irrational
r - s is irrational
r × s is irrational ( provided r ≠ 0 )
r ÷ s is irrational ( provided r ≠ 0 )

If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational.

Rationalising factors:  1. 2. 3. 