Number System For Bank Exams – Notes, Tips – Tricks And Questions
A number
system is defined as a systematic way of expressing numbers. The number system
is a mathematical notation for representing numbers of a given set by using a
set of digits or symbols in a logical manner. Number System helps to understand
the basics of quantitative ability.
The
value of any specific digit in a number can be determined by
- The actual
digit
- Its
position in the number
- The base of
the number system
Classification of Numbers:
The number system is classified into following
types:
Natural Numbers:
Numbers which are used for counting objects are
known as Natural numbers. The natural numbers are denoted by N.
N = {1, 2, 3, 4…………}
Whole Numbers:
Whole numbers are the set of numbers in which zero
is included in addition to natural numbers. The whole numbers are denoted by W.
W = {0, 1, 2, 3, 4…….}
Integers:
Integers include all natural numbers in addition
to zero & negative numbers. Integers are denoted by I or Z.
I = {-3, -2, -1, 0, 1, 2, 3…..}
Rational Numbers:
Rational numbers are expressed in the form of p/q
where ‘p’ & ‘q’ are integers and q≠0. They are denoted by Q.
Q = 5/6, 7/8 etc.
Irrational Numbers:
The numbers
which cannot be expressed in the form of p/q where ‘p’ & ‘q’ are integers
and q≠0. They are denoted by Q.
Example - π = 3.141592653589793238….
Prime Numbers:
A prime number is a natural number which is
divisible only by 1 and itself. It is greater than 0.
Example - 2, 3, 5, 7, 11, 31, etc.
Composite Numbers:
All the numbers (except 1) which do not fall under
the category of prime numbers are known as composite numbers.
Example - 4, 8, 10, 22, 100 etc.
Co-Prime Numbers:
Co-Prime Numbers are the set of integers which
have only 1 as their common factor or the highest common factor (HCF) is 1.
Example – 13 & 14 are co-prime.
Even Numbers:
The numbers which are divisible by 2 are known as
even numbers.
Example – 2, 4, 6, 8, 10….
Odd Numbers:
The numbers which are not divisible by 2 are known
as odd numbers.
Example – 3, 5, 7, 9……
Tricks to remember while solving number system
questions:
- 1 is
neither divisible nor prime.
- Two
consecutive odd prime numbers are known as prime pair.
- All natural
numbers are whole, integer, rational and real.
- All whole
numbers are rational, Integer and real.
- All
rational numbers incorporates integers, since every integer can be written
as a fraction with denominator 1. Example (9/1).
- The square of an even is even and the square of
an odd number is odd.
- Any given Prime Number can never be a Composite
Number.
- Fractions are rational.
- Zero is neither negative nor positive number.
- If x is any number then, if x divides zero,
result will be zero. If 0 divides x, then result will be infinite or not
defined or undetermined i.e. 0/x =0, but x/0 =∞ (infinite) where x is real
number.
- The sum and the product of two rational number
is always a rational numbers.
- The product or the sum of a rational number and
irrational number is always an irrational number.
