What are Real numbers?

What are Real numbers?|what are rational and irrational numbers|what are prime numbers?

Real number system

A real number is a number that can be found on the number line. These are the numbers that we normally use and apply in real-world applications.

 Below is a diagram of the real number system.

Real numbers are mainly classified into rational and irrational numbers.

A rational number is a number that can be written as a ratio of two integers. It can be a fraction, an integer, a whole number, or even a natural number.

Examples of rational numbers are

−523,−18,−4,0,37,9${\displaystyle -}$523,-18,-4,0,37,9

In the example,

−18is a rational number since it can be a ratio of integers -1 and 8.

9

           is a rational number since it can be a ratio of integers and 1.

0

00 is a rational number since it can be a ratio of integers 0 and 1.

For decimal numbers, it can be a rational number if it satisfies either one of the following:

•  It has finite number of digits.
  
  
•  Its digits are repeating in a continuous manner.
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• An irrational number is a number that cannot be written as a ratio of two integers. It is a non-terminating and non-repeating decimal.
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    Examples of irrational numbers are π,e,√2,-1.010010001.....

  
  
  In the example,
  
  
  π is an irrational number since it cannot be written as a ratio of two integers.
  
  
  0 is an irrational number since it cannot be written as a ratio of two integers.
  

  
  
  
  
  
  √an irrational number since it cannot be written as a ratio of two integers.
  
  
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• Classification of numbers

  Classification of rational number-

  The following are the classifications of rational numbers. 

  (i)  Natural numbers :

  N  =  { 1, 2, 3, 4, ...... }

  (ii)  Whole numbers :

  W  =  { 0, 1, 2, 3, ....... }

  (iii)  Integers :

  Z  =  {.........-2, -1, 0, 1, 2, 3, .........} 

  (iv)  Fractions :

  Examples : -1/2, 7/3, 3/4, 2 1/7

  (v)  Decimals :

  Examples : 0.2, -1.23, 0.0085

  (vi) Recurring decimal : 

  Examples : 0.333333......, 0.257257..........

  Other categories of number

  # According to the number of factors.

  
  

  1.Prime  number-Thenumber which

  has two factors that is 1 and the number itself.

  
  

  2.composite number-The number which has more than two factors .

  Here is the table of prime number 

  
  

  

  
  

  1 is neither a prime number nor a composite number.

  
  

  #according to the divisibility by 2

  1.even number-the number which is divisible by 2.eg. 2,4,6,8.....

  
  

  2.odd number-the number which is not divisible by 2.eg. 1,3,5,7.....
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