Lets say you have some apples and if somebody asks how many apples you have, what will you answer? One got to put a "label" on them. And here comes "numbers" to help you out. We need numbers to define the quantity and to perform mathematical operations like addition and subtraction. Numbers can classified in various depending on what they represent and where they are used. Here they are:
Natural Number
It all starts with counting.And how will counting start if you are counting your apples? You have to start with 1 and then go on. ( One doesn't have to count, if they have no apple to begin with).
Natural Numbers are those numbers that starts from 1, followed by 2,3 and so on.
Natural Numbers={1,2,3,4,5...}
Whole Number
Whole numbers are natural numbers with the inclusion of zero. Whole numbers starts from Zero, followed by 1, 2 and so on.
Whole Numbers = {0,1,2,3,4,...}
or Whole Numbers = 0 + Natural Numbers.
Integers
Integers are whole numbers plus the inclusion of negatives numbers from -1, -2, -3, and so on. Integers = Whole Numbers + { -1, -2, -3, -4, -5,...}Real Number
Number line is a line where we can represent the numbers and their fractional or decimal parts. A number lines start from 0 to either sides, both positive and negative and goes on till positive and negative infinity.Real Numbers are those numbers that can be represented on a number line.
Natural Numbers, Whole Numbers, Integers all belongs to Real Numbers.
Decimal Number
Decimal Numbers have an integer plus a decimal part or the fractional part.
For example, the number 15.02 is a decimal number having 15 as the integral part and the .02 as the fractional part.
Irrational Numbers
Irrational Numbers are the numbers that cannot be expressed on the number line. These numbers can't be expressed as a terminating decimal.For example, √2, ∛2,√3 are some of the irrational numbers.
Negative Numbers
Negative numbers have the same absolute value as a positive numbers, but with a different sign. For Example the absolute value of -5 and 5 is 5 but their sign is opposite.One can't see negative numbers in nature. One can observe that there are 5 cows in the field but one cannot say that there are -5 cows in the field. Negative numbers are used to represent opposing quantities.For example credit and debit, positive charge and negative charge.
For example, a credit $5 and debit of $5 adds to 0 because their absolute value is same but of opposite nature.
5 units positive charge and 5 units of negative charge adds to zero.
Prime Numbers
Prime number are those numbers that have only two divisors - the number 1 and the number itself. Example. 1,2,3,5,7,11... are some prime numbers. Try to divide these numbers using various divisors and you will know that they are only divided by the number 1 and the dividend itself.Special case of number 1: The number 1 is not a prime number. The smallest prime number is the number 2 not the number 1.
Composite Numbers
Any number that is not a prime number is a composite number.Example of composite numbers are 1,4,6,8,9,10,12,14,15,16,18,20,...These numbers have more than two divisors.Place Value
Place value is calculated by multiplying the digit whose place value is to be calculated and the place ( hundredth, thousandth etc..). for example: if we have to calculate the place value of 5 in the number 858412. Then first we have to decide the place at which 5 is located.Here wa can see that 5 have 4 digits on the right side. Therefore we have to multiply 5 by 10000 to get the place value. ( 5 x 10000 = 50000).An easier method is to discard all the digits before the digit whose place value we are calculating. For the above number we will discard 8 and we will left with 58412. Now replace all digits after the digit 5 to get the place value for the required digit. i.e. 58412 => 50000 .
Also Read: Difference Between Place Value and Face Value
Predecessor and successor
Predecessor of a number X is a number that comes 1 count before the number X. To get predecessor of number X
we have to subtract the number X by1. In the same way successor of a number X is number that immediately follows the number XExample: Predecessor of number 45 is (45 - 1)= 44 and the successor of 45 is (45 +1) =46.
The second number will be read as five crore three lakh twenty one thousand six hundred fifty four.
Addition ( + )
Commutative Property
We take a number 2 and added it to another number 8, the result is 10. Now, We take a number 8 and added it to another number 2, the result is again 10.
This property of addition, where addition of two numbers is always equal, irrespective of the order of addition is known as commutative property of addition.
a + b = b + c, where a and b are any two numbers.
Associative Property
We take a number 5 and added it to another number 9, the result is 14 and add the result of previous addition to 8 to arrive at 22. Now, We take a number 9 and add it to number 8 and the result of this addition is added to 5, the result is again 22.This property of addition, where addition of a group of number is always the same irrespective of order of the addition is known as associative property of Addition.
(a + b) + c = a + (b + c) , where a,b and c are numbers.
Subraction ( - )
We have,8 - 3 = 5
and3 - 8 = - 5
Therefore, Subtraction is not a commutative.
Multiplication ( x )
We have,8 X 3 = 24
and3 X 8 = 24
Therefore, Multiplication is commutative.
And(8 X 3) X 5 = 120
and3 X (8 X 5) = 120
Therefore, Multiplication is also associative.
Division ( ÷ )
We have,8 ÷ 4 = 2
and4 ÷ 8 = 0.5
Therefore, Division is not a commutative and obviously, not associative.
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