## Number Systems

CBSE Class 9 Maths

Important Points To Remember

① Counting numbers 1, 2, 3, 4... are called

**Natural Numbers**(

**N**)

②

**Whole Numbers**(

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

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

**Integers**(

**Z**).

④

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

⑤ Every rational number have either

__terminating__or

__repeating decimal representation__.

⑥ The decimal expansion of an irrational number is

__non-terminating__and

__non-repeating__.

⑦ There are

__infinitely many rational numbers__between any two given rational numbers.

⑧

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

⑨ All

__real numbers__can be represented on a number line. Every point on the number line represents a unique real number.

⑩ For every given positive real number x, we can find √x geometrically.

⑪ 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 )

⑫ If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational.

⑬ Rationalising factors:

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