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Number System (Classification (Real Number (Rational Number (Decimals…
Number System
Classification
Real Number
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Rational Number
Integers (+ve, -ve, non -ve)
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Conversion of decimal to P/Q form ex 0.33, 0.12525,0.12323
Shortcut for Conversion, Same Examples
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Composite Numbers defn, 3types of Natural Numbers
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Number of Factors
How to calculate number of factors for any number? e.g 24, 36 etc. (logic behind that) using prime factorization
Number of factors for Perfect Square numbers, generic form
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In how many ways can a number be represented by the difference of two natural numbers for both Odd and even number.
Divisibility Rule
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Rule of 6,12,18,144 (composite Numbers)
Using co-prime numbers
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Remainder Theorem
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Concept of cyclicity to determine the remainder of a number with high exponential power ex: (14^77 / 11)
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Defn of Cyclicity
Finding Unit's Place
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Cyclicity for 2,3,7,8
2^23, 2^129,14272^100, 3^87,121213^24
Unit place rule
2^n+8^n=0, 3^n+7^n=0, 4^n+6^n=0, 1^n+9^n=0, Imp only if n is odd
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Exponents and Indices
- While multiplying if bases are same powers are added
- While dividing if bases are same powers are subtracted
- Any base power to zero will be 1
- Any base with negative power will give reciprocal of number
- Power outside of power will multiply