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Maths > Number System > Flashcards

Number System Flashcards

1
Q

“Extension of the system” meaning

A

The process of enlarging a number system by preserving its Algebraic structure.

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2
Q

(-a) + (-b) =

A

-(a + b)

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3
Q

(-a) + b =

A

-(a-b) [If a is greater than b]

b-a [If b is greater than a]

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4
Q

In rational numbers (Q), there is no

A

NEXT GREATER NUMBER.

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5
Q

2 systems of logarithm

A

1) Common logarithm

2) Natural logarithm

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6
Q

Common logarithm

A

Base is 10.

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7
Q

Natural logarithm

A

Base is e.

e = 2.73 (approx)

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8
Q

Natural numbers also called

A

Counting numbers.

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9
Q

Even numbers definition

A

All INTEGERS divisible by 2.

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10
Q

Odd numbers

A

All INTEGERS which are not divisible by 2.

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11
Q

Even numbers are denoted by

A

“2n” where n is any INTEGER.

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12
Q

Odd numbers are denoted by

A

“2n - 1” where n is any INTEGER.

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13
Q

Integers are represented by the symbol

A

I or Z

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14
Q

Rational numbers

A

Numbers that can be expressed in the form “p/q” where q is not equal to 0.

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15
Q

Real numbers can be represented on the

A

Number line

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16
Q

All numbers on the number line are

A

Real numbers

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17
Q

Number line

A

Geometrically straight line with an arbitrary 0.

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18
Q

All prime numbers are

A

Natural numbers

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19
Q

Prime numbers

A

Natural numbers having 1 and itself as the factors.

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20
Q

Co prime numbers

A

Numbers whose HCF is 1.

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21
Q

Any 2 consecutive numbers would be co-prime.

A

T

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22
Q

Twin primes

A

Pairs of prime numbers having only one composite number between them. Eg (2,3) (3,5) etc

23
Q

Composite numbers

A

All natural numbers which are not prime.

24
Q

1 is neither prime nor composite

A

T

25
Q

Imaginary numbers

A

All the numbers whose square is negative.

Eg 3i.

26
Q

2 types of fractions

A

Common fractions

Decimal fractions

27
Q

Common fractions

A

Denominator is not equal to 10 or any power of 10.

28
Q

Decimal fractions :

A

Denominator is equal to 10 or any power of 10.

29
Q

Compound fraction

A

Fractions whose numerators and denominators are themselves fractions.

30
Q

A recurring decimal is of 2 types

A

Pure recurring decimals

Mixed recurring decimals

31
Q

Pure recurring decimals

A

All digits after the decimal point is repeated.

32
Q

Mixed recurring decimal

A

A recurring decimal is said to be mixed, if at least one of the digits after the decimal point is not repeated.

33
Q

Order in which brackets should be removed while solving an expression

A

First bracket to be removed : ()

In that order : ( ) { } [ ]

34
Q

When an expression contains a vinculum, then u have to solve that before using the BODMAS rule.

A

T

35
Q

Vinculum is also called as

A

Bar.

36
Q

All perfect squares are

A

Integers.

37
Q

Perfect squares (square numbers) defined as

A

An integer that is the square of an integer.

Eg 0

38
Q

Recurring decimals also called as …. or …..

A

Periodic decimal

Circulating decimal

39
Q

If (a/b) and (c/d) are 2 rational numbers then

(a+c)/(b+d) is btw those 2 numbers

A

T

40
Q

If y>x , then find n rational numbers btw them

A special way

A

Find “d” = (y-x)/(n+1)

Then the numbers are (x+d), (x+2d), (x+3d) …. (x+nd)

41
Q

Instead of the bar which we put over the period of the recurring decimal, we can put

A

Dots

42
Q

The repeating digit or the set of repeating digits in a recurring decimal is called the

A

Period of the recurring decimal

43
Q

In the period of a recurring decimal, the maximum number of dots that can be put is

A

2 dots.

44
Q

In a recurring, if only some part of the decimal part is repeating, then it is called

A

Mixed recurring decimal.

45
Q

How do you know if a rational number is terminating

A

If the denominator is a multiple of 2 or 5 then it is terminating.

46
Q

How to convert any recurring decimal into fraction

A

[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.

47
Q

If p*2 is divisible by 3, then p is divisible by

A

3.

48
Q

A rational number cannot have a common factor other than

A

1

49
Q

What is a surd

A

x - positive rational number
n - positive number
n√x - irrational number

Then n√x is a surd.

n√x : nth root of x

50
Q

Surd is also called as

A

Radical

51
Q

All surds are irrational numbers but all irrational numbers are not surds

A

T

52
Q

√5 can be termed as

A

A surd of order 2.

53
Q

When 2 surds are multiplied together such that their product is a rational number , then the 2 surds are called

A

Rationalising factors of each other.

54
Q

When 2 surds are multiplied together, they form a rational number these 2 surds are called

A

Rationalising factors of each other.

Maths (21 decks)

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