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# RD Sharma Solution for Class 9 Mathematics Chapter 1 - Number Systems

Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 9 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 1 - Number Systems.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 9 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 9 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

Exercise/Page

## RD Sharma Solution for Class 9 Mathematics Chapter 1 - Number Systems Page/Excercise 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.   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

Solution 1

Solution 2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Solution 3

Solution 1

Solution 2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

## RD Sharma Solution for Class 9 Mathematics Chapter 1 - Number Systems Page/Excercise 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.

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 ... ... ... 0.75075007500075000075 ... ... ...
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

## RD Sharma Solution for Class 9 Mathematics Chapter 1 - Number Systems Page/Excercise 1.5

Solution 1

(i) Real, rational, irrartional.

(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

Solution 1

Solution 2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

## Browse Study Material

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 1 - Number Systems for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 1 - Number Systems.

# Text Book Solutions

CBSE IX - Mathematics

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