# Class 9 RD SHARMA Solutions Maths Chapter 1 - Number Systems

Ex. 1.1

Ex. 1.2

Ex. 1.3

Ex. 1.4

Ex. 1.5

Ex. 1.6

1.40

1.41

1.42

## Number Systems Exercise Ex. 1.1

### Solution 1

Yes zero is a rational number as it can be represented in the form, where p and q are integers and q 0 as etc.

**Concept Insight:**Key idea to answer this question is "every integer is a rational number and zero is a non negative integer". Also 0 can be expressed in form in various ways as 0 divided by any number is 0. simplest is .### Solution 2

### Solution 3

There are infinite rational numbers in between 3 and 4.

3 and 4 can be represented as respectively.

3 and 4 can be represented as respectively.

Now rational numbers between 3 and 4 are

**Concept Insight:**Since there are infinite number of rational numbers between any two numbers so the answer is not unique here. The trick is to convert the number to equivalent form by multiplying and dividing by the number atleast 1 more than the rational numbers to be inserted.

### Solution 4

There are infinite rational numbers between

Now rational numbers between are

**Concept Insight**: Since there are infinite number of rational numbers between any two numbers so the answer is not unique here. The trick is to convert the number to equivalent form by multiplying and dividing by the number at least 1 more than the rational numbers required.

Alternatively for any two rational numbers a and b, is also a rational number which lies between a and b.

### Solution 5

(i) False

(ii) True

(iii) False

(iv)True

(v) False

(vi) False

(ii) True

(iii) False

(iv)True

(v) False

(vi) False

## Number Systems Exercise Ex. 1.2

### Solution 1

### Solution 2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

### Solution 3

## Number Systems Exercise Ex. 1.3

### Solution 1

### Solution 2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

## Number Systems Exercise Ex. 1.4

### Solution 1

### Solution 2

### Solution 3(i)

### Solution 3(ii)

### Solution 3(iii)

### Solution 3(iv)

### Solution 3(v)

### Solution 3(vi)

### Solution 3(vii)

### Solution 3(viii)

### Solution 3(ix)

### Solution 3(x)

As decimal expansion of this number is non-terminating non recurring. So it is an irrational number.

### Solution 3(xi)

Rational number as it can be represented in form.

### Solution 3(xii)

0.3796

As decimal expansion of this number is terminating, so it is a rational number.

As decimal expansion of this number is terminating, so it is a rational number.

### Solution 3(xiii)

As decimal expansion of this number is non terminating recurring so it is a rational number.

### Solution 3(xiv)

### Solution 4(i)

### Solution 4(ii)

### Solution 4(iii)

### Solution 4(iv)

### Solution 4(v)

### Solution 4(vi)

### Solution 5

### Solution 6

### Solution 7

### Solution 8

### Solution 9

### Solution 10

3 irrational numbers are -

0.73073007300073000073 ... ... ...

0.73073007300073000073 ... ... ...

0.75075007500075000075 ... ... ...

0.79079007900079000079 ... ... ...

0.79079007900079000079 ... ... ...

**Concept Insight: **There is infinite number of rational and irrational numbers between any two rational numbers. Convert the number into its decimal form to find irrationals between them.

Alternatively following result can be used to answer

Irrational number between two numbers x and y

### Solution 11

### Solution 12

### Solution 13

### Solution 14

## Number Systems Exercise Ex. 1.5

### Solution 1

(i) Real, rational, irrartional.

(ii) terminating, repeating.

(iii) terminating, non-terminating and reccuring.

(iv) rational, an irrational.

(ii) terminating, repeating.

(iii) terminating, non-terminating and reccuring.

(iv) rational, an irrational.

### Solution 2

(i) True

(ii) True

(iii) False

### Solution 3

### Solution 4

## Number Systems Exercise Ex. 1.6

### Solution 1

### Solution 2

## Number Systems Exercise 1.40

### Solution 1

### Solution 2

### Solution 3

### Solution 4

### Solution 5

### Solution 6

### Solution 7

### Solution 8

### Solution 9

## Number Systems Exercise 1.41

### Solution 10

### Solution 11

### Solution 12

### Solution 13

### Solution 14

### Solution 15

### Solution 16

### Solution 17

### Solution 18

### Solution 19

### Solution 20

## Number Systems Exercise 1.42

### Solution 21