Numbers, numbers system and classification of numbers for exams like ssc ibps bank po cleark railway etc...
Number System
Before understanding Number
system we have to know, what are Numbers?
Numbers: - we can say Numbers Are the collection of some certain symbols and figures which called Digit.
Every Number system has their unique symbols (Digits)
Then is many number systems,
but we used "Decimal Number System"
The Decimal Number System is
extended format Indo-Arabic Number system
It is, clear from the name
Indo-Arabic Number System is originated from India.
Place Value and Face Value
Every digit in a number has
their unique identity because of their place value and face valve
Face values - Face valve of a digit is digit itself
Place value - Place value of a digit is the value in which place digit is located in the number. Like Once Place, Tens Place, Hundred Place, thousand Place, Ten Thousand Place, Lack Place……etc. (Place Is Measured from the right Hand side of the number).
Ex- In number 25678 find the
place value and face value of 5.
Place value and face Value of 5
is
Face Value of 5:- Is 5 because
face value is the digit itself
Place value of 5:- is thousand
(1000)
So Identity or 5 written in
respect of given number: - 5×1000
Classification of Numbers
Natural Numbers: - These number are also called counting numbers as these are the numbers we use for counting purpose.
Natural numbers is represented
by N: (1, 2, 3, 4....)
Whole Numbers: - It includes all natural numbers, plus zero '0'.
Whole numbers denoted by w: (0, 1,
2, 3, 4, 5 …)
Integers: - It includes all whole numbers along with negative numbers.
It is Represented by I: (… -5,
-4, -3, -2, -1, 0, 1, 2, 3, 4, 5…)
Even numbers: - A number which is completely divisible by 2 is called even numbers. In other words, such number have 2 as a factor when they are written as a product of different numbers.
Examples:-30 = 2x3x5
Even numbers = 2, 4, 6, 8, 10, 12…… etc.
Odd numbers:- Are those numbers which are not completely divisible by 2.
For example: - 1, 3, 5, 7, 9…
Etc.
*Note-zero '0' is exception to
even and odd classification
Cyclic numbers: - It is such an integral of n digits, which on being multiplied by any number. From 1 ton, give a product containing the same n digits as in the original number and these digits are in the same cyclic order in the Product.
Example:- 5 X 2=10
5x3 = 15
5x4 =20
5x5 =25
Fraction: - A fraction is a number which represents a ratio or division of two integers. It is expressed in the form p/q where 'p' and q are integers 'p' is called numerator and 'q' is called the denominator.
*Note: Denominator never be zero
'0' q≠0
Example = 7/8, 8/13, 4/1
Real numbers: - Any measurement carried out in the physical world give some meaningful figure or value on the number. This number is called Real Number.
Real number consist two groups
(1) Rational numbers: - A rational number
can away be represented by a fraction of the form
p/q, when p and q are integers and q is not equal to zero (q≠0).
For example:-2=2/1, 2/3, 6/13...
(2) Irrational numbers: - An
irrational number cannot be expressed in the form of p/q where q≠0.
For example: √3, √2, Ï€=3.14.
Prime numbers: A prime number is a number which has no factors beside it self and unity (1).
For example: 2,3, 5, 7, 11,17, 19, 23, 29,31,37, 41,43, 47,
53,59,61,67,71,73,... Etc.
*Note largest prime number is
known is 22281 - 1 which about 700 digits is.
Decimal number: A collection of digits 10,112,399.9 after a period (point), is called decimal Fraction
For example: - 0.693, 0.53, 0.023 , 12/100=.12 etc.
COMMENTS