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# RD Sharma solutions for Class 9 Mathematics chapter 1 - Number Systems

## Chapter 1 : Number Systems

#### Page 5

Q 1 | Page 5

Is zero a rational number? Can you write it in the form p/q, where p and q are integersand q ≠ 0?

Q 2 | Page 5

Find five rational numbers between 1 and 2.

Q 3 | Page 5

Find six rational numbers between 3 and 4.

Q 4 | Page 5

Find five rational numbers between 3/5 and 4/5.

Q 5.1 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every whole number is a natural number.

Q 5.2 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every integer is a rational number.

Q 5.3 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every rational number is an integer.

Q 5.4 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every natural number is a whole number.

Q 5.5 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every integer is a whole number.

Q 5.6 | Page 5

State whether the following statement is true or false. Give reasons for your answers.

Every rational number is a whole number.

#### Pages 0 - 15

Express the following rational number as decimal:

42/100

Express the following rational number as decimal:

327/500

Express the following rational number as decimal:

15/4

Assuming that x, y, z are positive real numbers, simplify the following:

root5(243x^10y^5z^10)

Express the following rational number as decimal:

2/3

Express the following rational number as decimal:

-4/9

Express the following rational number as decimal:

-2/15

Express the following rational number as decimal:

-22/13

Express the following rational number as decimal:

437/999

Express the following rational number as decimal:

33/26

Look at several examples of rational numbers in the form p/q (q≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Simplify (3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)

#### Page 22

Q 1.1 | Page 22

Express the following decimal in the form p/q : 0.39

Q 1.2 | Page 22

Express the following decimal in the form p/q : 0.750

Q 1.3 | Page 22

Express the following decimal in the form p/q : 2.15

Q 1.4 | Page 22

Express the following decimal in the form p/q:

7.010

Q 1.5 | Page 22

Express the following decimal in the form p/q: 9.90

Q 1.6 | Page 22

Express the following decimal in the form p/q: 1.0001

Q 2.1 | Page 22

Express the following decimal in the form p/q: 0.bar4

Q 2.2 | Page 22

Express the following decimal in the form p/q: 0.bar37

Q 2.3 | Page 22

Express the following decimal in the form p/q: 0.bar54

Q 2.4 | Page 22

Express the following decimal in the form p/q: 0.bar621

Q 2.5 | Page 22

Express the following decimal in the form p/q: 125.bar3

Q 2.6 | Page 22

Express the following decimal in the form p/q: 4.bar7

Q 2.7 | Page 22

Express the following decimal in the form p/q: 0.4bar7

#### Pages 30 - 31

Q 1 | Page 30

Define an irrational number ?

Q 2 | Page 30

Explain, how irrational numbers differ from rational numbers ?

Q 3.01 | Page 30

Examine, whether the following number are rational or irrational:

sqrt7

Q 3.02 | Page 30

Examine, whether the following number are rational or irrational:

sqrt4

Q 3.03 | Page 30

Examine, whether the following number are rational or irrational:

2+sqrt3

Q 3.04 | Page 30

Examine, whether the following number are rational or irrational:

sqrt3+sqrt2

Q 3.05 | Page 30

Examine, whether the following number are rational or irrational:

sqrt3+sqrt5

Q 3.06 | Page 30

Examine, whether the following number are rational or irrational:

(sqrt2-2)^2

Q 3.07 | Page 30

Examine, whether the following number are rational or irrational:

(2-sqrt2)(2+sqrt2)

Q 3.08 | Page 30

Examine, whether the following number are rational or irrational:

(sqrt2+sqrt3)^2

Q 3.09 | Page 30

Examine, whether the following number are rational or irrational:

sqrt5-2

Q 3.1 | Page 30

Classify the following number as rational or irrational :-

sqrt23

Q 3.11 | Page 30

Classify the following number as rational or irrational :-

sqrt225

Q 3.12 | Page 30

Classify the following number as rational or irrational :-

0.3796

Q 3.13 | Page 30

Classify the following number as rational or irrational :-

7.478478...

Q 3.14 | Page 30

Classify the following number as rational or irrational :-

1.1010010001...

Q 4.1 | Page 30

Identify the following as rational or irrational number. Give the decimal representation of rational number:

sqrt4

Q 4.2 | Page 30

Identify the following as rational or irrational number. Give the decimal representation of rational number:

3sqrt18

Q 4.3 | Page 30

Identify the following as rational or irrational number. Give the decimal representation of rational number:

sqrt1.44

Q 4.4 | Page 30

Identify the following as rational or irrational number. Give the decimal representation of rational number:

sqrt(9/27)

Q 4.5 | Page 30

Identify the following as rational or irrational number. Give the decimal representation of rational number:

-sqrt64

Q 4.6 | Page 30

Identify the following as rational or irrational number. Give the decimal representation of rational number:

sqrt100

Q 5.1 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

x2 = 5

Q 5.2 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

y2 = 9

Q 5.3 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

z2 = 0.04

Q 5.4 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

u^2=17/4

Q 5.5 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

v2 = 3

Q 5.6 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

w2 = 27

Q 5.7 | Page 31

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

t2 = 0.4

Q 6 | Page 31

Give two rational numbers lying between 0.232332333233332... and 0.212112111211112.

Q 7 | Page 31

Give two rational numbers lying between 0.515115111511115... and 0.535335333533335...

Q 8 | Page 31

Find one irrational number between 0.2101 and 0.222... = 0.bar2

Q 9 | Page 31

Find a rational number and also an irrational number lying between the numbers 0.3030030003... and 0.3010010001...

Q 10 | Page 31

Find three different irrational numbers between the rational numbers 5/7" and "9/11.

Q 11.1 | Page 31

Give an example of two irrational numbers whose:

difference is a rational number.

Q 11.2 | Page 31

Give an example of two irrational numbers whose:

difference is an irrational number.

Q 11.3 | Page 31

Give an example of two irrational numbers whose:

sum is a rational number.

Q 11.4 | Page 31

Give an example of two irrational numbers whose:

sum is an irrational number.

Q 11.5 | Page 31

Give an example of two irrational numbers whose:

product is an rational number.

Q 11.6 | Page 31

Give an example of two irrational numbers whose:

product is an irrational number.

Q 11.7 | Page 31

Give an example of two irrational numbers whose:

quotient is a rational number.

Q 11.8 | Page 31

Give an example of two irrational numbers whose:

quotient is an irrational number.

Q 12 | Page 31

Find two irrational numbers between 0.5 and 0.55.

Q 13 | Page 31

Find two irrational numbers lying between 0.1 and 0.12.

Q 14 | Page 31

Prove that sqrt3+sqrt5 is an irrational number.

#### Pages 35 - 36

Q 1.1 | Page 35

Complete the following sentence:

Every point on the number line corresponds to a _________ number which many be either _______ or ________.

Q 1.2 | Page 35

Complete the following sentence:

The decimal form of an irrational number is neither ________ nor _________

Q 1.3 | Page 35

Complete the following sentence:

The decimal representation of a rational number is either ______ or _________.

Q 1.4 | Page 35

Complete the following sentence:

Every real number is either ______ number or _______ number.

Q 2.1 | Page 36

Find whether the following statement is true or false.

Every real number is either rational or irrational.

Q 2.2 | Page 36

Find whether the following statement is true or false.

π is an irrational number.

Q 2.3 | Page 36

Find whether the following statement is true or false.

Irrational numbers cannot be represented by points on the number line.

Q 3 | Page 36

Represent sqrt6, sqrt7, sqrt8 on the number line.

Q 4 | Page 36

Represent sqrt3.5, sqrt9.4, sqrt10.5 on the real number line.

#### Page 39

Q 1 | Page 39

Visualise 2.665 on the number line, using successive magnification.

Q 2 | Page 39

Visualise the representation of 5.3bar7 on the number line upto 5 decimal places, that is upto 5.37777.

## RD Sharma solutions for Class 9 Mathematics chapter 1 - Number Systems

RD Sharma solutions for Class 9 Maths chapter 1 (Number Systems) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 by R D Sharma (2018-19 Session) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Mathematics chapter 1 Number Systems are Introduction of Real Number, Irrational Numbers, Real Numbers and Their Decimal Expansions, Representing Real Numbers on the Number Line, Operations on Real Numbers, Laws of Exponents for Real Numbers.

Using RD Sharma Class 9 solutions Number Systems exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

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