Number System Flashcards
(29 cards)
Types of numbers
- Real no.
- Complex or Imaginary no.
Complex no. can also be called as
Imaginary no.
Imaginary no. can also be called as
Complex no.
What is real no. with ex
Real no. which can be represent in no. line and no’s whose sq is positive.
Real no. are of 2 types
- Rational
- Irrational
What is imaginary no. with ex
No’s that can’t be represent in no. line and no. whose sq is -ve
Ex: (√-2)^2 = -2, (√-1)^2 = -1
Types of real no.
Rational no. & Irrational no.
What Rational no. with example
can be return in p/q form where q is not equal to 0
Example: 2/3, 5/14, 7/11, 5, 2, 3
Terminating or Non terminating and recurring decimal no.
Example for terminating and non terminating and recurring decimal no.
2/5 = 0.4
256/1000 = 0.256
0.3(dash above 3) = 0.3333…
0.137(dash above 137) = 0.137137137137…
What is Irrational no.
Can’t be written in p/q form
√3, √5, √2, 3√5, π & NTNR
Example for irrational no.
√2 = 1.414…
√3 = 1.732…
√5 = 2.236…
π = 3.142…
These are NTNR
Types of rational no. with ex
- Fraction
1/2, 3/5, 7/9 - Intigers
Positive and Negative integers
…-4, -3, -2, -1, 0, 1, 2, 3, 4… - Decimals
Terminating Decimals
NTR Decimals
Zero can also be said as
Neutral integer
Non +ve integer
Non -ve integer
Integers does not includes
Fraction or decimal
All whole no’s are integer, right
Yes all whole numbers are inside the set of integers. In other words not all integers are whole no.
But integers also include negative numbers, which whole numbers do not.
Difference between natural and whole no
Natural no: 1, 2, 3, 4…
Whole no: 0, 1, 2, 3, 4…
Draw the diagram of number system structure and provide a rough map
= Number ⊂ Real no & Complex / Imaginary No
= Real no ⊂ Rational & Irrational no
- Rational - Termination or NTR decimal no
- Irrational - NTNR decimal no
= Rational no ⊂ Integer
= Integer ⊂ Zero, Positive & Negative
= Integers ⊂ Wholeno (Zero & Natural no) ⊂ Naturalno (1, 2, 3, 4…)
= Positive Integer ⊂ Odd, Even, Prime, Composite, Co-Prime, Perfect no, and Twin Primes are types or combinations of natural numbers
What is non natural no
Zero,
Negative integers,
Fraction,
Decimal
What is Co Prime, example
No whose HCF is 1, ex: (13,5), (5,18), (4,9), (9,14), (5,18)
It do not need to be prime themselves.
Two no whose HCF is 1 is called as
Co Prime
Difference between Co Prime and Twine Prime
= Co prime:
- No whose HCF is 1.
- It do not need to be prime themselves.
ex: (13,5), (5,18), (4,9), (9,14), (5,18)
= Twin Prime:
- Both numbers in the pair must be prime, and difference = 2
- Not all prime numbers are part of twin prime pairs but all paired numbers must be a prime
ex: (3,5), (5,7), (11,13)
ex for not a Co Prime no: (7,9), (13,15)
What is Twin Prime, example
Both numbers in the pair must be prime, and difference = 2
Not all prime numbers are part of twin prime pairs.
ex: (3,5), (5,7), (11,13)
ex for not a Co Prime no: (7,9), (13,15)
Even x Odd will be
Odd
Draw Divisor, Quotient, Dividend, Remainder
What is Divisor
5/2 = 5 - Dividend, 2 - Divisor = Dividend/Divisor
