1. SUBMITTED TO:
JITENDRA SIR

2. NUMBERS AS WE KNOW ARE
MATHEMATICAL OBJECTS USED
FOR COUNTING OR MEASURING.
IN THIS PRESENTATION WE WILL
LEARN ABOUT DIFFERENT SETS OF
NUMBERS, TOGETHER CALLED
NUMBER SYSTEM.

3. Numbers can be classified into 6 types.
These are:
1. Natural Numbers
2. Whole Numbers
3. Integers
4. Rational numbers
5. Irrational Numbers
6. Real Numbers

4. While counting, the numbers we normally use are called
Natural Numbers. Therefore, they are also known as
Counting Numbers. The counting numbers start with 1
and their end is not defined. They are denoted by “N”.
Apple Two Oranges Five Bananas Hundred Mangoes
For example:

5. The only difference between natural and whole numbers
is that the whole numbers have zero(0) included in it.
Therefore we can say that whole numbers are natural
numbers with zero at their starting. They are denoted by
“W”.
Examples of Whole Numbers:

6. When we add the whole numbers to the negatives of
natural numbers (-4,-3,-2,-1 ,etc.), we get a new set of
numbers known as Integers. The starting as well as the
end of integers is not defined. Integers are denoted by
“Z”.
Examples of Integers:Examples of Integers

7. When we divide a cake into 2 equal parts, the
parts cannot be written in forms of integers. So, in
such cases fractions are used. Fractions are parts
of whole numbers. A fraction consists of a
numerator and a denominator.
Examples of Integers::

8. You may have seen certain numbers like - 0.5, 1.7,
5.2, etc.[with a dot sign known as decimal point].
Such numbers are called decimal numbers. When
we divide numerator by denominator in fractions
which are not completely divisible using a dot[.]
sign, we get decimal numbers.
Examples of Decimals:

9. Any number written in fractional form where the
numerator and the denominator are both
integers and the denominator is not zero is
called a Rational Number. Rational numbers,
when written as decimals have a fixed value
which ends or repeats after a certain number of
digits. They are denoted by “Q”.

10. The numbers which cannot be written in the form
of a fraction where the numerator and the
denominators are integers and the denominator is
not zero because their decimal expansion is never
ending and never repeating are known as
Irrational Numbers. Rational Numbers are
denoted by “S”.
Examples of Irrational Numbers:

11. Rational and irrational numbers together form a
new set of numbers called Real Numbers. In short,
all the other number systems listed earlier are a
part of it. Real Numbers are denoted by “R”.