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

Practise This Question

The bar graph below gives the strength of 'section A' consecutively for 6 years since 2009, when it was Class 6, Sec. A. Each year, same students get promoted to next class. Also, some of the students get new admission and some of the students get transferred. So, the number of students varies accordingly.

How many students got admitted to the class at the start of session 2012 if nobody from the previous year batch took a transfer and 2 students were not promoted?