 # What are Real numbers ? All numbers Explained

## What are Real Numbers ?

Real numbers are those numbers which can be represented on Number line. In easiest way we can say Real Number is collection of Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers, Prime numbers, Composite numbers, Decimal numbers and almost all other numbers which we can think of.

### What are Natural Numbers ?

Natural Numbers are the numbers which starts from ONE i.e 1, 2, 3, 4, 5, 6, 7, 8 . . . and so on.

### What are Whole Numbers ?

Whole numbers are same as Natural numbers but they start from ZERO i.e 0, 1, 2, 3, 4, 5, 6, 7, 8 . . . and so on.

### What are Integers ?

Integers are the positive and negative Whole Numbers which means Integers are . . . ,-4, -3, -2, -1, 0, 1, 2, 3, 4, 5 . . .
Integers do not contain any decimal or fractional values.

### What are Rational Numbers?

Rational numbers are those numbers which can be written in the form of p/q. For example 3/2, 5/7, 8/5, 3, 5, 6, 0.5, 3.25 etc. I know you must be thinking that WHY I have included 3, 5, 6, 0.5, 3.25 in rational numbers as they are not in the form of p/q.
Here is the reason –
We can write 3 as 3/1 because any number divided by 1 results the same number and similarly 5 = 5/1 and 6 = 6/1. We all know 0.5 can be written as 5/10 by removing decimal and similarly 3.25 can be written as 325/100. And so all these numbers are known as Rational numbers as they can be written in the form of p/q.
Rational numbers can also be negative i.e -3/2, – 5/7, – 3, – 4, -3.5, -4.53 etc.

### What are Irrational Numbers ?

Irrational numbers are those numbers which can not be written in the form of p/q, we can also say the numbers which are not Terminating (cannot be ended) are called Irrational numbers. For example √2, √3, √5 1.56745352423657563… etc. Now you must be thinking we can also write √2 as √2/1, so we should call it rational.
But NO here is the reason- (You Have To Watch The Video Given Below to Understand it Properly)
We know √2 is a non terminating number i.e value of √2 can not be ended. √2 = 1.4142135623730950488016887242096980785696718753769. . .
So by dividing it by 1 we cannot call it as Rational because Numerator part of it is Irrational (√2/1 = 1.4142135623730950488016887242096980785696718753769. . . / 1). Its Numerator part is Irrational as it Cannot be ended.

### What are Prime Numbers ?

Prime numbers are those numbers which have exactly two factors that is 1 and itself. For Example 13 is a prime number because it has only two factors 13 = 13 x 1.
Similarly 2, 3, 5, 7, 11, 13, 17, 19, 23, . . . all are prime numbers as they all have only two factors that is 1 and itself.
2 = 2 x 1
3 = 3 x 1
5 = 5 x 1
7 = 7 x 1
11 = 11 x 1
13 = 13 x 1
17 = 17 x 1
19 = 19 x 1
23 = 23 x 1
.
.
.

### What are Composite Numbers ?

Numbers which are not Prime are Composite Numbers.
Numbers like 4, 6, 8, 10, 12, 14, 15 etc are not prime because all of them have factors other than 1 and itself.
4 = 2 x 2 x 1 (4 has factors other than 1 and 4)
6 = 2 x 3 x 1 (6 has factors other than 1 and 4)
15 = 3 x 5 x 1 (6 has factors other than 1 and 4)

Important Note 1 is neither prime nor composite Numbers

ALL THESE NUMBERS WHICH ARE EXPLAINED ABOVE ARE CALLED REAL NUMBERS BECAUSE THEY CAN BE REPRESENTED ON NUMBER LINE.

If you are still reading this educational article then I want to give you some Extra Knowledge.
After working with Real Numbers our Mathematicians stuck in some problems when they saw numbers like √-3, √-5, √-7 (all Negative numbers with root). They have not dealt with these numbers earlier, so they called them IMAGINARY NUMBERS.

## What are Imaginary Numbers ?

Numbers like √-3, √-5, √-7 which are negative numbers with root are called Imaginary numbers.
Mathematician introduced a term IOTA (i) which is equal to √-1.
IOTA (i) = √-1
By using this value of Iota we can write √-2 = √-1 × √2 = √2 i (because i = √-1)
Similarly √-5 = √5 i
√-7 = √7 i
√-8 = √8 i

## What are Complex Numbers ?

Complex Numbers are small extension to real numbers that is If we add Imaginary numbers to Real numbers then the resulting number is called Complex Number or in simple words we can say Complex numbers are sum of Real numbers and Imaginary numbers.
Complex Number = Real number + Imaginary number
For Example Real number given = 3 and Imaginary number given = √5 i
So Complex number = 3 + √5 i