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Number System in Maths

Numbers are the fundamental concepts of Maths. Numbers are used regularly in our life. They are also called numerals. Numbers are used to count objects or people in a group. Numbers are also used to state measurements of different quantities such as time, distance, velocity, weight, etc.

The properties of numbers make them fit for performing number-crunching procedures on them. These numbers are communicated in numeric structures and furthermore in words. For instance, 2 is composed as two in words, 25 is composed as 25 in words, and so on Understudies can work on composing the numbers from 1 to 100 in words to find out additional..

Definition of Numbers

Numbers are the arithmetic values that are used to express the quantity and perform mathematical calculations. The examples of numbers are 0, 1, 4, 10, 99, -19, etc.

There are many variations in numbers based on the value they express. It is not necessary that all the numbers are used to express the same type of quantity. For example, ‘i’ is an expression used to represent complex numbers in Mathematics, whereas ‘N’ is used to represent the natural numbers. Let us learn here the classification of different types of numbers.

Classification of Numbers

There are various types of numbers in Maths that are used for calculation. The list of the numbers are:

  • Natural and Whole numbers
  • Rational and Irrational numbers
  • Even and Odd numbers
  • Real and Imaginary numbers

Let us discuss all the numbers here.

Natural and Whole numbers

Natural numbers are those positive numbers that start from 1 and end at infinity.


Whole numbers are all the positive integers from 0 to infinity.


Rational and irrational numbers

The numbers that can be represented in the form of numerator and denominator, such as, P/Q, where P and Q are any integers and Q is not equal to zero, are called rational numbers. These numbers are terminating and sometimes repeating. Examples are, ½, ¾, 1/10, etc.

Irrational numbers cannot be expressed in the form of numerator and denominator. It is non-terminating and non-repeating. √2, √3, √5, Pi, Euler’s number, etc., are the examples of irrational numbers.

Even and Odd Numbers

The numbers that are evenly or exactly divisible by 2 are the even numbers. They are commonly represented as 2n, where n is any natural number. Examples of even numbers:

4, 8, 10, 28, 320, 88, 64, 1222, etc.

The numbers that are not divisible by 2, evenly, then they are called odd numbers. If a number resembles the standard form of 2n+1, where n is any natural number, then it is an odd number. The examples are: 1, 5, 9, 17, 29, 35, 77, etc.

Real and Imaginary numbers

Real numbers are all those numbers that can be expressed and calculated upon. These numbers include all positive or negative integers, decimal or fractions, rational or irrational, natural or whole numbers.Imaginary numbers are the numbers that cannot be used for mathematical calculations in our daily life. Usually, the imaginary number is expressed using the alphabets ‘i’ or ‘j’.

i = √-1

The combination of real and imaginary numbers are called complex numbers. It is represented in the form of A+iB, where A is a real number and B is an imaginary number. Apart from these, there are many concepts that are directly or indirectly related to Mathematical operations.


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