Thursday, September 24, 2015

Number System: 15 types of Numbers and concepts related to it

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:

  1. “0” is the only whole number which is not Natural Number
  2. Every Natural Number is a Whole Number. In other words Natural Numbers are subset of Whole Numbers.
  3. 1 Million = 106 = Ten lac
  4. 1 Billion = 10= 100 crore
Hope the article will be useful in your upcoming IBPS PO, IBPS clerk and all other examinations.

Location: India

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