Number System Flashcards
“Extension of the system” meaning
The process of enlarging a number system by preserving its Algebraic structure.
(-a) + (-b) =
-(a + b)
(-a) + b =
-(a-b) [If a is greater than b]
b-a [If b is greater than a]
In rational numbers (Q), there is no
NEXT GREATER NUMBER.
2 systems of logarithm
1) Common logarithm
2) Natural logarithm
Common logarithm
Base is 10.
Natural logarithm
Base is e.
e = 2.73 (approx)
Natural numbers also called
Counting numbers.
Even numbers definition
All INTEGERS divisible by 2.
Odd numbers
All INTEGERS which are not divisible by 2.
Even numbers are denoted by
“2n” where n is any INTEGER.
Odd numbers are denoted by
“2n - 1” where n is any INTEGER.
Integers are represented by the symbol
I or Z
Rational numbers
Numbers that can be expressed in the form “p/q” where q is not equal to 0.
Real numbers can be represented on the
Number line
All numbers on the number line are
Real numbers
Number line
Geometrically straight line with an arbitrary 0.
All prime numbers are
Natural numbers
Prime numbers
Natural numbers having 1 and itself as the factors.
Co prime numbers
Numbers whose HCF is 1.
Any 2 consecutive numbers would be co-prime.
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Twin primes
Pairs of prime numbers having only one composite number between them. Eg (2,3) (3,5) etc
Composite numbers
All natural numbers which are not prime.
1 is neither prime nor composite
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Imaginary numbers
All the numbers whose square is negative.
Eg 3i.
2 types of fractions
Common fractions
Decimal fractions
Common fractions
Denominator is not equal to 10 or any power of 10.
Decimal fractions :
Denominator is equal to 10 or any power of 10.
Compound fraction
Fractions whose numerators and denominators are themselves fractions.
A recurring decimal is of 2 types
Pure recurring decimals
Mixed recurring decimals
Pure recurring decimals
All digits after the decimal point is repeated.
Mixed recurring decimal
A recurring decimal is said to be mixed, if at least one of the digits after the decimal point is not repeated.
Order in which brackets should be removed while solving an expression
First bracket to be removed : ()
In that order : ( ) { } [ ]
When an expression contains a vinculum, then u have to solve that before using the BODMAS rule.
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Vinculum is also called as
Bar.
All perfect squares are
Integers.
Perfect squares (square numbers) defined as
An integer that is the square of an integer.
Eg 0
Recurring decimals also called as …. or …..
Periodic decimal
Circulating decimal
If (a/b) and (c/d) are 2 rational numbers then
(a+c)/(b+d) is btw those 2 numbers
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If y>x , then find n rational numbers btw them
A special way
Find “d” = (y-x)/(n+1)
Then the numbers are (x+d), (x+2d), (x+3d) …. (x+nd)
Instead of the bar which we put over the period of the recurring decimal, we can put
Dots
The repeating digit or the set of repeating digits in a recurring decimal is called the
Period of the recurring decimal
In the period of a recurring decimal, the maximum number of dots that can be put is
2 dots.
In a recurring, if only some part of the decimal part is repeating, then it is called
Mixed recurring decimal.
How do you know if a rational number is terminating
If the denominator is a multiple of 2 or 5 then it is terminating.
How to convert any recurring decimal into fraction
[decimal part]
Numerator: Total no of digits - no of non recurring digits
Denominator: no of 9s equal to number of recurring digits and no of 0’s equal to number of non recurring digits.
If p*2 is divisible by 3, then p is divisible by
3.
A rational number cannot have a common factor other than
1
What is a surd
x - positive rational number
n - positive number
n√x - irrational number
Then n√x is a surd.
n√x : nth root of x
Surd is also called as
Radical
All surds are irrational numbers but all irrational numbers are not surds
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√5 can be termed as
A surd of order 2.
When 2 surds are multiplied together such that their product is a rational number , then the 2 surds are called
Rationalising factors of each other.
When 2 surds are multiplied together, they form a rational number these 2 surds are called
Rationalising factors of each other.
