Hi Friends,
Let me introduce you to a
basic but very important topic NUMBER
SYSTEM. All the government exam
aspirants must have through knowledge of this topic. Almost all the Quantative
Aptitude or Numerical Ability books start with this topic so you must have read
the topic earlier, but I am sure still you will find some missing points here.
Look at the image above which is a Number system hierarchy divided into 15 types, Lets go in details of each
type.
Numbers are mainly devided in two types.
- Imaginary Numbers : Any Number multiplied by i ( where i = √-1 )
- Real Numbers : everything except imaginary numbers.
Point to remember: Imaginary numbers have this i , and the value of i is root of minus one. We
can not find the root of minus (negative) numbers, and that’s the reason
imaginary numbers are shown as multiples of i.
Real Numbers
Lets go in further details of
Real Numbers, they are divided in
- Rational Numbers : are numbers that can be written as a ratio (x/y) . This includes all the fractions and whole numbers. (note: whole numbers can be shown as ratio of number itself and 1, so they are also rational numbers)
- Irrational Numbers: can be written as decimals but not as a fraction. Irrational numbers have endless digits to the right of decimal point. (e.g. π=3.141592…, √2=1.414213….)
Rational Numbers
Rational Numbers are
further divided into
- Integers : Integers are Integrals, they contain no fractional or decimal parts. (….-3,-2,-1,0,1,2,3…)
- Non Integers : non integers are of two type, Fractions (x/y) and Decimals (5.56)
Integers
Integers are further
contain following types.
- Whole Numbers: All non negative integers are whole numbers. (0,1,2,3…)
- Negative Integers: Integers which are not whole numbers (….,-3,-2,-1)
Whole Numbers
Whole Numbers are further divided to below mentioned
types.
- Even Numbers : are numbers divisible by 2.
- Odd Numbers: are numbers not divisible by 2.
- Prime Numbers: are numbers that have only two factors one is the number itself and another is ‘1’. These numbers are not divisible by another numbers except 1.
- Composite Numbers: are numbers that have more than two factors.
“Prime Numbers Up to 100: 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”
How to find out whether given number ( X>100 ) is prime or not?
Suppose given
number is ”X”, then find a smallest square number nearly greater than “X”.
Lets say “Y”
is a nearest square number, check the divisibility of all the prime numbers
less than √Y, if “X” is not divisible by any
prime number less than √Y then X is a prime
number.
e.g. Say
given number is X= 191
then
smallest square greater than X is Y=196
so √Y=14
Now prime
numbers less than 14: 2,3,5,7,11,13
Now check
divisibility of X=191 by all above prime numbers.
Its not
divisible by any of above numbers so 191 is a prime number.
Place value & Face value:
Face Value of a digit is a value of digit itself. In Decimal number system the
value of a digit depends on its place. The value of digit is 10 times higher
than same number placed on right side before decimal point.
e.g. 834 = 800 + 30 + 4
here a place value of 8 is
800, while that of 3 is 30, and of 4 is 4. While face value of the three digits
remain same 8,3 and 4.
Co-primes: Two Numbers are
said to be co-primes if their HCF is 1.
Important Points to remember:
- “0” is the only whole number which is not Natural Number
- Every Natural Number is a Whole Number. In other words Natural Numbers are subset of Whole Numbers.
- 1 Million = 10^{6 }= Ten lac
- 1 Billion = 10^{9 }= 100 crore
Hope the article will be useful in your upcoming IBPS PO, IBPS clerk and all other examinations.
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