This document discusses different types of numbers. It begins with counting numbers which start from 1 and have no largest number. Natural numbers also start from 1 and are infinite. Whole numbers include 0 and are also infinite. Integers include both positive and negative numbers and have an equal and opposite number for every integer. Rational numbers are numbers that can be represented as fractions. Real numbers include both rational numbers like fractions as well as irrational numbers like pi which have non-terminating, non-repeating decimals. The real number set contains all other number sets.

1. 





NUMBER
SYSTEM in our
The NUMBERS play vital role
life.
Counting Numbers begin from 1
The smallest Number is 1
Next number, called Successor is
obtained by adding 1 to the number
However there is NO largest Number.
Number 0 stands for

2. NATURAL NUMBERS
The NATURAL NUMBERS begin from 1
1 is smallest NATURAL NUMBER
There is NO largest NATURAL NUMBER
NATURAL NUMBERS are INFINITE
1
2
3
4
5
6
7

3. WHOLE NUMBERS
The WHOLE NUMBERS begin from 0
The smallest WHOLE NUMBER is 0
There is NO largest WHOLE NUMBER
WHOLE NUMBERS are INFINITE
0
1
2
3

4. INTEGERS
The INTEGERS are spread on BOTH
sides of 0
The INTEGER 0 is neither POSITIVE nor
NEGATIVE
NEGATIVE numbers lie on the LEFT of 0 &
POSITIVE numbers lie on the RIGHT of 0
For every + ve INTEGER x , there is
a – ve INTEGER -x
-3
-2
-1
0
1
2
3

5. RATIONAL NUMBERS
A Number of the form p / q where p & q
are INTEGERS and q ≠ 0, is called a
RATIONAL NUMBER
A RATIONAL NUMBER is POSITIVE OR
NEGATIVE OR ZERO
RATIONAL NUMBERS are EVERY
WHERE DENSE ie in between any two
given RATIONAL NUMBERS infinitely
many RATIONAL NUMBERS can be
placed

6. TERMINATING DECIMALS


The Rational
Numbers whose
Denominator has
ONLY 2 & 5 as its
FACTORS , is always
TERMINATING.
Numerator divided
by Denominator ,
gives Remainder
Zero




7 / 50 is a Rational
Number
D = 50
50 = 2 x 5 x 5
Hence , 7 / 50 is
Terminating

7. NON-TERMINATING REPEATING
DECIMALS


The Rational
Numbers whose
Denominator has
FACTORS other
than 2 & 5 , is
always NONTERMINATING.
Numerator divided
by Denominator ,
gives Remainder
other than Zero


1 / 3 has 3 as
Denominator
Numerator divided
by Denominator
gives Value as
0 . 33 3 . . .
 The repeating of 3
NEVER
terminates

8. NON-TERMINATING NON
REPEATING DECIMALS


The Numbers in
which Numerator
divided by
Denominator is
NOT regular , are
IRRATIONAL
NUMBERS
The values of π , √2
& √3 etc are
IRRATIONAL
NUMBERS

π = 3.14……………


√2=1.414………….
√3
=1.732………….

9. IRRATIONAL NUMBERS
The numbers
which are NOT
RATIONAL, are
IRRATIONAL
NUMBERS
 The NONTERMINATING
NON REPEATING
DECIMALS are
called
IRRATIONAL
NUMBERS

IRRATIONAL
NUMBERS
 π = 3.14…
 √2=1.414…
 √3=1.732…
 The repeating of
Decimal does
NOT terminate


10. REAL NUMBERS
The RATIONAL NUMBERS
&
IRRATIONAL NUMBERS
together are called as
REAL NUMBERS
REAL NUMBER set is the
LARGEST
set