PPT: Numbers And Number System | Quantitative Techniques for CLAT PDF Download

 Page 1


Number System
Page 2


Number System
What is Number System?
Definition
The number system or the 
numeral system is the 
system of naming or 
representing numbers. It 
provides a structured way to 
denote quantities and 
perform mathematical 
operations.
Types
There are various types of 
number systems in 
mathematics like binary, 
decimal, etc. Each system 
has unique properties and 
applications in different 
fields.
Importance
Understanding number systems is crucial for solving 
mathematical problems, developing computational algorithms, 
and advancing scientific research across disciplines.
Page 3


Number System
What is Number System?
Definition
The number system or the 
numeral system is the 
system of naming or 
representing numbers. It 
provides a structured way to 
denote quantities and 
perform mathematical 
operations.
Types
There are various types of 
number systems in 
mathematics like binary, 
decimal, etc. Each system 
has unique properties and 
applications in different 
fields.
Importance
Understanding number systems is crucial for solving 
mathematical problems, developing computational algorithms, 
and advancing scientific research across disciplines.
Numbers and Number System
1
Numerals
A group of figures is called a numeral. Examples 
include 15, 955, -10, -2, and 2.
2
Natural Numbers
The numbers we use for counting natural objects are 
known as natural numbers, denoted by N = (1, 2, 3, 
4, 5, 6 ...). Zero is not a natural number.
3
Whole Numbers
On including zero (0) in natural numbers, we get 
whole numbers, denoted by W = (0, 1, 2, 3, 4 ...).
4
Even and Odd Numbers
Numbers divisible by 2 are even (2, 4, 6...), and 
numbers not divisible by 2 are odd (1, 3, 5...), 
expressed as 2k and 2k-1 respectively, where k is 
any natural number.
Page 4


Number System
What is Number System?
Definition
The number system or the 
numeral system is the 
system of naming or 
representing numbers. It 
provides a structured way to 
denote quantities and 
perform mathematical 
operations.
Types
There are various types of 
number systems in 
mathematics like binary, 
decimal, etc. Each system 
has unique properties and 
applications in different 
fields.
Importance
Understanding number systems is crucial for solving 
mathematical problems, developing computational algorithms, 
and advancing scientific research across disciplines.
Numbers and Number System
1
Numerals
A group of figures is called a numeral. Examples 
include 15, 955, -10, -2, and 2.
2
Natural Numbers
The numbers we use for counting natural objects are 
known as natural numbers, denoted by N = (1, 2, 3, 
4, 5, 6 ...). Zero is not a natural number.
3
Whole Numbers
On including zero (0) in natural numbers, we get 
whole numbers, denoted by W = (0, 1, 2, 3, 4 ...).
4
Even and Odd Numbers
Numbers divisible by 2 are even (2, 4, 6...), and 
numbers not divisible by 2 are odd (1, 3, 5...), 
expressed as 2k and 2k-1 respectively, where k is 
any natural number.
Types of Numbers
Prime Numbers
Numbers divisible only by 1 and 
itself, like 2, 3, 5, 7, 11. Note that 1 is 
not a prime number as it doesn't 
have two divisors.
Composite Numbers
Numbers other than 1 which are not 
prime. These have divisors other 
than 1 and themselves.
Consecutive & Integers
Consecutive numbers increase by 
one (e.g., 7, 8, 9). Integers include all 
positive and negative whole 
numbers and zero, denoted by I 
(e.g., -5, -4, -3, -2, -1, 0, 1, 2, 3...).
Page 5


Number System
What is Number System?
Definition
The number system or the 
numeral system is the 
system of naming or 
representing numbers. It 
provides a structured way to 
denote quantities and 
perform mathematical 
operations.
Types
There are various types of 
number systems in 
mathematics like binary, 
decimal, etc. Each system 
has unique properties and 
applications in different 
fields.
Importance
Understanding number systems is crucial for solving 
mathematical problems, developing computational algorithms, 
and advancing scientific research across disciplines.
Numbers and Number System
1
Numerals
A group of figures is called a numeral. Examples 
include 15, 955, -10, -2, and 2.
2
Natural Numbers
The numbers we use for counting natural objects are 
known as natural numbers, denoted by N = (1, 2, 3, 
4, 5, 6 ...). Zero is not a natural number.
3
Whole Numbers
On including zero (0) in natural numbers, we get 
whole numbers, denoted by W = (0, 1, 2, 3, 4 ...).
4
Even and Odd Numbers
Numbers divisible by 2 are even (2, 4, 6...), and 
numbers not divisible by 2 are odd (1, 3, 5...), 
expressed as 2k and 2k-1 respectively, where k is 
any natural number.
Types of Numbers
Prime Numbers
Numbers divisible only by 1 and 
itself, like 2, 3, 5, 7, 11. Note that 1 is 
not a prime number as it doesn't 
have two divisors.
Composite Numbers
Numbers other than 1 which are not 
prime. These have divisors other 
than 1 and themselves.
Consecutive & Integers
Consecutive numbers increase by 
one (e.g., 7, 8, 9). Integers include all 
positive and negative whole 
numbers and zero, denoted by I 
(e.g., -5, -4, -3, -2, -1, 0, 1, 2, 3...).
Some Properties of Numbers
1
Natural Numbers
Sum and product of two natural numbers is always a natural number. However, difference and division may not always yield natural 
numbers.
2
Integers
Sum, difference and product of two integers is always an integer, but division may produce non-integer results.
3
Rational Numbers
Sum, difference, product and quotient of two rational numbers remain rational. Rational number 0 is the additive identity (x + 0 = x), and 1 
is the multiplicative identity (a × 1 = a).
4
Irrational Numbers
Sum, difference, product and quotient of two irrational numbers may or may not be irrational. The sum or difference of a rational and an 
irrational number is always irrational.