Number System. "To preserve my brains I want food and this is now my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship." - Srinivasa Ramanujan (Indian Mathematician) A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures. It also allows us to operate arithmetic operations like addition, subtraction and division.

2. •Number System is a method of representing Numbers
on the Number Line with the help of a set of Symbols
and rules.
•These symbols range from 0-9 and are termed as digits.
•Number System is used to perform mathematical
computations ranging from great scientific calculations
to calculations like counting the number of toys etc.
Number System in Mathematics

3. A Number line is a representation of Numbers with a fixed
interval in between on a straight line. A Number line contains
all the types of numbers like natural numbers, rationals,
Integers, etc. Numbers on the number line increase while
moving Left to Right and decrease while moving from right to
left. Ends of a number line are not defined i.e., numbers on a
number line range from infinity on the left side of the zero to
infinity on the right side of the zero.
Number Line

5. Numbers that are represented on the
right side of the zero are termed as
Positive Numbers. The value of
these numbers increases on moving
towards the right. Positive numbers
are used for Addition between
numbers.
𝒆𝒙𝒂𝒎𝒑𝒍𝒆: 𝟏, 𝟐, 𝟑, …
Positive
Numbers

6. Numbers that are
represented on the left side
of the zero are termed as
Negative Numbers. The
value of these numbers
decreases on moving
towards the left. Negative
numbers are used for
Subtraction between
numbers.
𝑒𝑥𝑎𝑚𝑝𝑙𝑒 ∶ −1, −2, −3, …
Negative
Numbers

7. Numbers are of various types depending upon the
patterns of digits that are used for their creation.
Various symbols and rules are also applied on
Numbers which classifies them into a variety of
different types:

9. Natural Numbers are the most basic type of Numbers
that range from 1 to infinity. These numbers are also
called Positive Numbers or Counting Numbers. Natural
Numbers are represented by the symbol 𝑁.
Example: 1, 2, 3, 4,...

10. Whole Numbers are basically the Natural Numbers,
but they also include ‘zero’. Whole numbers are
represented by the symbol W.
Example: 0,1, 2, 3, 4, ...

11. Integers are the collection of Whole Numbers plus
the negative values of the Natural Numbers.
Integers do not include fraction numbers i.e. they
can’t be written in a/b form. The range of Integers is
from the Infinity at the Negative end and Infinity at
the Positive end, including zero. Integers are
represented by the symbol Z.
Example: …,-3, -2, -1 , 0, 1, 2, 3, …

12. Fractions are the numbers that are written in the form
of a/b, where, a belongs to Whole numbers and b
belongs to Natural Numbers, i.e., b can never be 0.
The upper part of the fraction i.e. a is termed as a
Numerator whereas the lower part i.e. b is called
Denominator.
Example: 1/2, 3/4, 13/6, ...

13. Rational numbers are the numbers that can be
represented in the fraction form i.e. a/b. Here, a
and b both are integers and b≠0. All the
fractions are rational numbers but not all the
rational numbers are fractions.
Example: 1/3 ,5/8, 0.34, ...

14. Irrational numbers are the numbers that can’t be
represented in the form of fractions i.e. they can not
be written as a/b.
Example: 2 , 𝜋, …

15. Real numbers are the numbers that can be represented
in the decimal form. These numbers include whole
numbers, integers, fractions, etc. All the integers
belong to Real numbers but all the real numbers do not
belong to the integers.

16. Imaginary Numbers are all those numbers that are not
real numbers. These numbers when squared will result in
a negative number. The √-1 is represented as i. These
numbers are also called complex numbers.
Example: −2 , −6

17. Numbers that do not have any factors other than 1
and the number itself are termed as Prime
Numbers.
Example: 2, 3, 5, 7, 11, 13, ...

18. All the numbers other than Prime Numbers are
termed as Composite Numbers except 0. Zero is
neither prime nor a composite number.
Example: 4, 6, 8, ...