Number System PDF

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

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.

Whole Numbers on Number line

Interesting fact:

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


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

Integers on the Number line

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 will also fall under this category. Example: 0.083333…. = 1 / 12
  • All integers are rational numbers

Irrational Numbers

  • A number that cannot be written as a 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 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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