1. NUMBERS
IMPORTANT FACTS AND FORMULAE
I..Numeral
: In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
called
digits
to represent any number.
A group of digits, denoting a number is called a
numeral.
We represent a number, say 689745132 as shown below :
Ten
Crores
(10
8
)
Crore
s(10
7
)
Ten
Lacs
(Millions
) (10
6
)
Lacs(
10
5
)
Ten
Thous
ands
(10
4
)
Thous
ands
(10
3
)
Hundr
eds
(10
2
)
Ten
s(1
0
1
)
Uni
ts(1
0
0
)
6
8
9
7
4
5
1
3
2
We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred
and thirty-two'.
II
Place Value or Local Value of a Digit in a Numeral
:
In the above numeral :
Place value of 2 is (2 x 1) = 2; Place value of 3 is (3 x 10) = 30;
Place value of 1 is (1 x 100) = 100 and so on.
Place value of 6 is 6 x 10
8
= 600000000
III.Face Value
: The
face
value
of a digit in a numeral is the value of the
digit itself
at whatever place it may be. In the above numeral, the face value of 2 is 2; the face value
of 3 is 3 and so on.
IV.TYPES OF NUMBERS
1.Natural Numbers
: Counting numbers 1, 2, 3, 4, 5,.
.... are called
natural
numbers.
2
.
Whole Numbers
: All counting numbers together with zero form the set of
whole
numbers
.
Thus,
(i)
0 is the only whole number which is not a natural number.
(ii)
Every natural number is a whole number.
3
.
Integers
: All natural numbers, 0 and negatives of counting numbers
i.e.,
{…, - 3 , - 2 , - 1 , 0, 1, 2, 3,….
.} together form the set of integers.
(i)
Positive Integers
: {1, 2, 3, 4, ….
.} is the set of all positive integers.
(ii)
Negative Integers
:
{-
1, - 2, - 3,….
.} is the set of all negative integers.
(iii)
Non-Positive and Non-Negative Integers
: 0 is neither positive nor
negative. So, {0, 1, 2, 3,….} represents the set of non-negative integers, while
{0, - 1 , - 2 , - 3 , ….
.} represents the set of non-positive integers.
4.
Even Numbers :
A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8,
10, etc.
5.
Odd Numbers :
A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7,
9, 11, etc.
6.
Prime Numbers :
A number greater than 1 is called a prime number, if it has exactly
two factors, namely 1 and the number itself.
Prime numbers upto 100 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97.