Download 1 Natural numbers- 2 Whole Numbers- 3 Integers

Class – VI
1
NUMBER SYSTEM
Natural numbersCounting numbers started by 1 are called “Natural numbers”
The set of natural numbers is denoted as
N = { 1, 2, 3, ……………}
2
Whole NumbersNatural numbers including “0” (zero) are called whole numbers
The set of whole numbers is
W = { 0, 1, 2, 3 ……….}
3
IntegersWhole numbers including natural numbers with negative sign are called “Integers”
The set of integers is
I or Z = { ………-3, -2, -1, 0, 1, 2, 3 …………}
(a) Odd numbers – 1, 3, 5, 7, …………
(b) Even numbers- 0, 2, 4, 6, …………
(c) Prime number- Number divisible by one and itself only 2, 3, 5, 7, 11, 13, 17…..
4
Rational NumbersNumber of the form p/q where p, q I and q  0 are called rational numbers.
p

Q   , p & q are integers & q  0
q

Decimal form of rational numbers
(i)
The number of digits are finite after decimal (Terminating decimal)
For example – (a) -0.5
(b)
3.654
(ii)
5
The number of digits are infinite after decimal and repetition of the digits are
there (non-terminating, recurring decimal)
For example – (a) 1.525252.......... ....  1.52
(b) 2.148148148........  2.148
Irrational numbersNumbers which are non-terminating, non-recurring are called irrational numbers.
Example- 2, 3, 7
The most popular irrational numbers
(i)
  3.1459265.......... ......
(ii)
e  2.7182818.......... .......
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Some results on irrational numbers:
1
Negative of an irrational number is an irrational number.
2
SUM, DIFFERENCE, PRODUCT & QUOTIENT of a rational and an irrational
number is an irrational number.
3
SUM, DIFFERENCE, PRODUCT & QUOTIENT of two irrational numbers
may be rational or an irrational number.
6
Real numbersNumbers including rational and irrational numbers are called “real numbers”
Representation of real numbers on numbers line.
-4
-3 -2
-1
0
1
2
3
4
5
Each and every point on the line represents a definite real number
Each and every real number has definite chair on number line.
All real numbers can be represented on a number line.
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________________________________________________________________________________________
Address : 61, First Floor, Chanakya Plaza, New CG Road, Chandkheda, Ahmedabad
Contact : 96017 55017 , 90999 66717
www.abhigyanam.com