NUMBER SYSTEM

Types of Number ----1. Natural Number

                                         2. Whole Number

                                         3. Integer Number

                                         4. Rational Number

                                         5. Irrational Number

 

NATURAL NUMBER

a Number which is started from 1 is called Natural Number.

Like- 1, 2, 3, 4, 5, 6 continue…

 

WHOLE NUMBER

 a number which is started from 0 is called Whole Number.( 0 + 1,2,3,4,5…….)= Whole number

Like -0,1,2,3,4,5,6,7,8,9,………

 

Whole Number are 4 Types –    1.Even Number

                                                                   2.Odd Number

                                                                   3.Prime Number

                                                                   4.Composite Number.

      ·       Even Number :- a Number which is divisible by 2 its called Even Number

Ex- 2,4,6,8,10,12,14,16……(Divisible by 2)

     ·       Odd Number :- Number which doesn’t divided by 2 its called Odd Number.

Ex- 1,3,5,7,9,11,13…..(doesn’t divided by 2)

     ·       Prime Number :- a number which has no factor other than 1 and itself.

Ex- 2, 3, 5, 7, 11, 13, 17, 19 (Divided by 1 or Itself)

     ·       Composite Number :- a number which has more than one factor other than 1 and the number itself.

Ex- 4 (factor 1,2,4) 1 and 4 is common but 2 also divisible so that’s composite

      6 (factor 1,2,3,6) 1 and 6 common but 2,3 is extra factor

Note- 1 is neither Prime Number nor Composite Number.

INTEGER NUMBER

A number that can be Positive , Negative or Zero that’s call Integer Number

Ex- -3,-2,-1,0,1,2,3,4,5…………….

RATIONAL NUMBER

Any Number that can be expressed in the form of P/Q, where P,Q are Integer and Q ≠ 0

Ex- 0,1,2,3,4,5,-1,-2,-3,-4,-5

 

IRRATIONAL NUMBER

Any Number that cannot be expressed in the form of P/Q that’s called Irrational Number.

Ex- 1.121212. 2.252525 also Root 5, root 3,

 

---------------------------------------------------------------------------------------

CBSE BOARD

Class-9 maths NCERT chapter 1, Exercise no-1.1 introduction

 

Type of Real Number ?

Real Number are Two Types

1.      With Decimal

2.      Without Decimal

With Decimal Number Or Point Numbers

Terminate Numbers like (1.2, 1.5, 1.1, 2.5, 8.9, 1.25, 2.46, 5.65 these all number are ended)

Non-Terminate Numbers like (1.12121212, 2.25252525 Numbers are repeated and not ended)

Non-Terminate non-Repeating Numbers like (1.123456 , 2.321564 Numbers are not ending and not repeating)

Terminate and No-Terminate numbers are called Rational Number.

Rational Numbers represented as = p/q ( p & q are integers, here q value never will be 0) q≠0

Non-Terminate and non-Repeating Number are Called Irrational Number

Root 2, root 3 , root 5 , root 7 is Non Terminate and Non-Repeating Number

 

 

Without Decimal Number  or Integers

         ·       .....-5, -4, -3, -2, -1 ,  0  , 1, 2, 3, 4, 5,……..

  

         ·       ……, -5 , -4, -3, -2, -1 are Negative Integers

 

 

         ·       0 called Zero Integers

 

         ·       1 , 2, 3, 4, 5 ……… are Positive Integers Or Natural Number

 

 

         ·       Positive Integers are various type name like- Natural Numbers (Called Natural Number because these are Counting Number)

 

         ·       Zero Number + Positive Number equal to Whole Number.

Like (0 , 1 , 2 , 3 , 4 , 5 ……These are Whole Number)

---------------------------------------------------------------------------------------

 

Question and Answer

1.    Is Every Whole Number is Natural Number ?

-         No, Every Whole number is not Natural Number. Because here include Zero Integers Or 0 Numbers.

Natural number is – 1 , 2, 3, 4, 5 ……

 

2.    Is Every Integers Are Rational Number ?

-         Yes every Integers are Rational Number. Because Integers number is  -3 , -2, -1 , 5, 6, 7     or   -3/1, -2/1. -1/1, 5/1, 6/1, 7/1  (form of P/Q, Q≠0)

-          Note- All Integers can be represented as Rational Number.

 

3.    Is Every Rational Number are Integers ?

No, Every Rational Number is not Integers Number.

4.    0 are Rational Number ?

Yes

5.    Every Natural Numbers are Whole Number ?

Yes

6.    Is Every Integers are Whole Number ?

No.. Because include negative number like(-1, -2, -3)

7.    Every Rational Number are Whole Number ?

No.

 

 

 

 

 

 

 

CBSE BOARD 9^TH MATH.