Number System

Question 1

“Extension of the system” meaning

Answer 1

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

Question 2

(-a) + (-b) =

Answer 2

-(a + b)

Question 3

(-a) + b =

Answer 3

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

b-a [If b is greater than a]

Question 4

In rational numbers (Q), there is no

Answer 4

NEXT GREATER NUMBER.

Question 5

2 systems of logarithm

Answer 5

1) Common logarithm

2) Natural logarithm

Question 6

Common logarithm

Answer 6

Base is 10.

Question 7

Natural logarithm

Answer 7

Base is e.

e = 2.73 (approx)

Question 8

Natural numbers also called

Answer 8

Counting numbers.

Question 9

Even numbers definition

Answer 9

All INTEGERS divisible by 2.

Question 10

Odd numbers

Answer 10

All INTEGERS which are not divisible by 2.

Question 11

Even numbers are denoted by

Answer 11

“2n” where n is any INTEGER.

Question 12

Odd numbers are denoted by

Answer 12

“2n - 1” where n is any INTEGER.

Question 13

Integers are represented by the symbol

Answer 13

I or Z

Question 14

Rational numbers

Answer 14

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

Question 15

Real numbers can be represented on the

Answer 15

Number line

Question 16

All numbers on the number line are

Answer 16

Real numbers

Question 17

Number line

Answer 17

Geometrically straight line with an arbitrary 0.

Question 18

All prime numbers are

Answer 18

Natural numbers

Question 19

Prime numbers

Answer 19

Natural numbers having 1 and itself as the factors.

Question 20

Co prime numbers

Answer 20

Numbers whose HCF is 1.

Question 21

Any 2 consecutive numbers would be co-prime.

Answer 21

T

Question 22

Twin primes

Answer 22

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

Question 23

Composite numbers

Answer 23

All natural numbers which are not prime.

Question 24

1 is neither prime nor composite

Answer 24

T

Question 25

Imaginary numbers

Answer 25

All the numbers whose square is negative. | Eg 3i.

Question 26

2 types of fractions

Answer 26

Common fractions | Decimal fractions

Question 27

Common fractions

Answer 27

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

Question 28

Decimal fractions :

Answer 28

Denominator is equal to 10 or any power of 10.

Question 29

Compound fraction

Answer 29

Fractions whose numerators and denominators are themselves fractions.

Question 30

A recurring decimal is of 2 types

Answer 30

Pure recurring decimals | Mixed recurring decimals

Question 31

Pure recurring decimals

Answer 31

All digits after the decimal point is repeated.

Question 32

Mixed recurring decimal

Answer 32

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

Question 33

Order in which brackets should be removed while solving an expression

Answer 33

First bracket to be removed : () | In that order : ( ) { } [ ]

Question 34

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

Answer 34

T

Question 35

Vinculum is also called as

Answer 35

Bar.

Question 36

All perfect squares are

Answer 36

Integers.

Question 37

Perfect squares (square numbers) defined as

Answer 37

An integer that is the square of an integer. | Eg 0

Question 38

Recurring decimals also called as .... or .....

Answer 38

Periodic decimal | Circulating decimal

Question 39

If (a/b) and (c/d) are 2 rational numbers then (a+c)/(b+d) is btw those 2 numbers

Answer 39

T

Question 40

If y>x , then find n rational numbers btw them | A special way

Answer 40

Find “d” = (y-x)/(n+1) | Then the numbers are (x+d), (x+2d), (x+3d) .... (x+nd)

Question 41

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

Answer 41

Dots

Question 42

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

Answer 42

Period of the recurring decimal

Question 43

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

Answer 43

2 dots.

Question 44

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

Answer 44

Mixed recurring decimal.

Question 45

How do you know if a rational number is terminating

Answer 45

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

Question 46

How to convert any recurring decimal into fraction

Answer 46

[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.

Question 47

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

Answer 47

3.

Question 48

A rational number cannot have a common factor other than

Answer 48

1

Question 49

What is a surd

Answer 49

x - positive rational number n - positive number n√x - irrational number Then n√x is a surd. n√x : nth root of x

Question 50

Surd is also called as

Answer 50

Radical

Question 51

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

Answer 51

T

Question 52

√5 can be termed as

Answer 52

A surd of order 2.

Question 53

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

Answer 53

Rationalising factors of each other.

Question 54

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

Answer 54

Rationalising factors of each other.