Image result for numbers and their classification


 Numbers:- A number is a mathematical object used to count, measure and label. Ex.-1,2,3,4 etc

Classification of numbers:-


                                               



                                                    

Description of different types of numbers:-

Natural number:- Natural numbers are those used for counting (as “there are four coins on the table.”) and ordering (as “this is the fifth largest city in the country.”) Ex.:- 1, 2, 3, 4, 5 etc.

Real number:- A real number is a value of a continuous quantity that can represent a distance along a line. Ex:- 0, 1, √3, -7 etc.

Rational number:- A rational number is any number that can be expressed as the quotient or fraction p/q of two integers , a numerator p and a  non-zero denominator q. Moreover any repeating or terminating decimal represents a rational number. Ex:- 0, 1, 3/4, -7/5 etc.

Irrational number:- An irrational number is a number that cannot be expressed as a fraction p/q for any integer p and q. Irrational number has decimal expansions neither terminate nor become periodic. Ex:- π(=3.14159…), √3, √21 etc.

Whole number:- The whole numbers are the natural numbers together with zero.

Integer:- An integer is a whole number that can be positive negative or zero. Ex:- 0, 1, -2 etc.
                                     

                                    


                            BLOCK DIAGRAM OF CLASSIFICATION OF NUMBERS

Fractional numbers:-   A fraction represents a part of a whole consisting of a numerator and a denominator. Ex:- ½, -3/4, 21/11 etc.

Proper fraction:-A proper fraction is a fraction where the numerator (the top number of a fraction) is less than the denominator (the bottom number of a fraction). Ex:- ½, ¼, ¾ etc.

Improper fraction:- An improper fraction is a fraction where the numerator is greater than the denominator. Ex:- 21/11, 49/36 etc.

Negative number:- A negative number is a real number that is less than zero. Ex:- -√5, -3, -5/8 etc.

Positive number:- A positive number is a real number that is greater than zero. Ex:- 11, 17/23, √3 etc.

Even number:- An even number is an integer which is “evenly divisible” by 2. This means that if the integer is divided by 2, it yields no remainder. Ex:-0, 2, 4, 6, 14 etc.
*Zero is an even number because zero divided by two equals zero, which is an integer.

Odd number:- An odd number is an integer which is not a multiple of 2 i.e. when divided by two the integer leaves a remainder. Ex:- 3, 13, 29 etc.

Prime number:- A prime number is a whole number greater than 1 whose only factors are 1 and itself. Ex:-  2, 3, 5, 37, 97 etc.
*2 is the only even number which is a prime number.

Composite number:- A composite number is an integer greater than 1 which has factors other than 1 and itself.
*1 is neither a prime nor a composite number.

Co-prime number:- Two integers a and b are said to be relatively prime or co-prime if the only positive number that divides both of them is 1. This is equivalent to the greatest common divisor (g.c.d) being 1.

Perfect number:- A perfect number is a positive integer that is equal to the sum of its positive divisors excluding  the number itself
(also known as its aliquot sum).
Ex:- 6, 28, 496 etc. Proper divisors of 6 are 1, 2, 3. Aliquot sum of 6 is 1 + 2 + 3 = 6 which is equal to the number itself.

Complex number:- A complex number is a number that can be expressed in the form of a + bi, where a and b are real numbers and ’i’ is an imaginary number.
Ex:- √(-1), √(-43), √(-97) etc.


The video given below describes very lively about the classification of numbers.