Basic Of Number System
1. If digit is at Unit Place just Multiply with One (As name Unit Place)
2. If digit is at Tens Place just Multiply with Ten(As name Tens Place)
3. If digit is at Hundred Place just Multiply with Hundred (As name Hundred Place)
Note: So By using this concept you can write any Number into Equivalent form.
Type of Numbers:
Trick to find out whether given Number is Prime Number or Not?
Composite Number: The natural Numbers which are not Prime, are called Composite Numbers.
example: 222, 246, 6668.etc
Co-Prime Number: Two natural Numbers x, y are said to be Co-Prime if there HCF
(Highest Common factor) is 1 (One).example: (2,3), (4,5), (7,9), (8,11) ....etc. are Co-Prime Number.
Checking Divisibility of Numbers
Divisibility By 2: Any number is divisible by 2 if and only if its Unit place has value 0,2,4,6,8.
example: 757575757757570, 454546, 9999999999999992, 1234567890 etc.
All are divisible by 2. Since contain 0, 6, 2, 0 at Unit place in above examples.
Divisibility By 4: A number is divisible by 4 if the number formed by its last Two Digit is divisible by 4.
Example: 1234516, 5656720, 77777777777728, 99999999932 etc.
here in example 16, 20, 28, 32 are last Two digit and divisible by 4, so whole number is Divisible by 4.
Divisibility By 8: A number is divisible by 8 if the number formed by Hundred's, Ten's and Unit's Digit of the given Number is divisible by 8.
Example: 765756352, 8578969352 etc.
here in example 352 is at Hundred's, Ten's and Unit's place and divisible by 8, so whole number is Divisible by 8.
Divisibility By 5: A number is Divisible by 5 only when it's Unit Digit is 0 or 5.
Example: 574747470, 456464445, 9888990 etc.
here in example 0 or 5 is at Unit's place and divisible by 5, so whole number is Divisible by 5.
Divisibility By 10: A number is Divisible by 10 only when it's Unit Digit is 0.
Example: 646464890, 44445770, 81123450 etc.
here in example 0 is at Unit's place and divisible by 10, so whole number is Divisible by 10.
Divisibility By 3: A number is Divisible by 3 only when the Sum of Digits is Divisible by 3.
Example: 123, 4563, 555 etc.
Here Sum of Digit: 1+2+3=6 and we know 6 is Divisible by 3 so 123 is also Divisible by 3.
Here Sum of Digit: 4+5+6+3=18 and we know 18 is Divisible by 3 so 4563 is also Divisible by 3.
Basic Of Real Number
Terminating decimal expansion: If any real number is in p/q form and their Quotient is terminated at certain time, called Terminating decimal expansion.
Example: 3/8=0.375, 13/125=0.104, 7/80=0.0875, 14588/625=23.3408 etc. look their Quotient after certain time Terminated.
Non-Terminating Repeating: If any real number is in p/q form and their Quotient is non-terminated and repeating form, called Non-Terminating Repeating.
Example: 1/7= 0.1428571428571............Non-Terminated and Repeating.
same as 1/3=0.333333333333333.........Non-Terminated and Repeating.
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