 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. Interesting fact:

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

2.Integers:

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. 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