Number System PDF

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

Classification of Number System (PDF)

The natural numbers are classified as follows:

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.

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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.

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The set of integers is represented by the symbol Z.

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

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

Real Numbers

  • The set of all the rational and irrational numbers are called real numbers
  • Represented by the symbol R

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 the 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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