CBSE Class 9 - Maths - Number Systems - Important Points To Remember (#cbsenotes)

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: