Number System PDF

Number system can be defined as the collection of numbers. Below are the types of number systems:

  1. Natural numbers:

Natural numbers or counting numbers starting from 1,2,3,…. are the most familiar numbers. They are symbolically represented by N. Natural numbers together with 0 are called whole numbers.

Number System

Interesting fact:

Sum of two natural numbers is a natural number. Also, product of two natural numbers is a natural number.


Natural numbers are the subset of integers. Natural numbers without zero are called positive integers and when written with a negative sign are called as negative integers.

Number System

The set of integers is represented by the symbol Z.

  1. Rational numbers:
  • A fraction with an integer numerator and a positive integer in the denominator. It is represented in the form of p / q where p and q are integers and q is not equal to zero
  • Decimal numbers which have a repeating pattern after some point also fall under this category. Example: 0.083333…. = 1 / 12
  • All integers are rational numbers
  1. Irrational numbers:
  • A number that cannot be written as fraction i.e p / q
  • It is a never ending number and does not repeat itself in the decimal form. Example: π = 3.14159…
  • This was first discovered by the Pythagorean in Greece
  1. Real numbers:
  • The set of all the rational and irrational numbers are called real numbers
  • Represented by the symbol R
  1. Prime numbers:
  • Any real number that is divisible by 1 and itself come under this category
  • Example of prime numbers 1,2,3,5,7,11…

Further classification of number system is as follows

  • Decimal
  • Binary
  • Octal
  • Hexadecimal

To learn more about their types and classification download the Number system pdf

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