Class 9th Number System
basic concepts and important results
1. Natural Numbers (N) :
Counting numbers are known as natural numbers. Thus 1, 2, 3, 4, …etc. are natural numbers.
˜ The first and the least natural number is 1 (one)
˜ Consecutive natural nos. differ by 1 (one).
2. Whole numbers (w) :
All natural numbers together with '0' form whole numbers. Thus 0, 1, 2, 3, 4, … etc. one are whole nos.
˜ The first and the least whole number is zero.
˜ Consecutive whole number differe by one.
3. Integers (I or Z) :
All natural nos. 0 and negative of natural nos. form integers for example. ……–4, –3, –2, –1, 0, 1, 2, 3, 4, … etc.
˜ O is neither a negative nor a positive number. It is a neutral no.
4. Prime numbers (P) :
A natural number, which is greater than 1 and divisible by one and by itself only, is called a prime number. For eg : 2, 3, 5, 7, 11, ……
˜ The smallest prime number is 2
˜ Except 2 ; all other prime nos. are odd.
5. Composite number (C) :
A natural number, which is greater than 1 and is not prime, is called a composite number. Thus 4, 6, 8, 9, 10, 12, 14, ……
˜ The smallest composite number is 4.
˜ A composite number can be even or odd.
˜ It has atleast three distinct factor.
6. Co-prime numbers :
If two numbers do not have any factor (other than 1) common; the numbers are said to be co-prime
Thus (i) 6 and 25 are coprime, no any common factor other than 1. (ii) 3 and 5 are co-prime, no any common factor other than 1.
˜ It is not necessary that any of the two co-prime numbers has to be prime also.
˜ All consecutive nos. are coprime.
7. Terminating decimals :
The decimal expansion ends after a finite number of steps of division. Such decimal expansions are called terminating decimals
For example : = 0.4, = 4.125 and so on.
8. Non-terminating decimals :
The decimal expansions never come to an end. Such decimal expansions are called non-terminating
For example = = 0.1818…, =0.3555……
9. Rational Numbers (Q) :
The numbers of the form , where p and q are integers and q ¹ 0, are known as rational numbers.
or
A number is rational if and only if it
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