#### Chapters

Chapter 2: Exponents of Real Numbers

Chapter 3: Rationalisation

Chapter 4: Algebraic Identities

Chapter 5: Factorisation of Algebraic Expressions

Chapter 6: Factorisation of Polynomials

Chapter 7: Linear Equations in Two Variables

Chapter 8: Co-ordinate Geometry

Chapter 9: Introduction to Euclid’s Geometry

Chapter 10: Lines and Angles

Chapter 11: Triangle and its Angles

Chapter 12: Congruent Triangles

Chapter 13: Quadrilaterals

Chapter 14: Areas of Parallelograms and Triangles

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Heron’s Formula

Chapter 18: Surface Areas and Volume of a Cuboid and Cube

Chapter 19: Surface Areas and Volume of a Circular Cylinder

Chapter 20: Surface Areas and Volume of A Right Circular Cone

Chapter 21: Surface Areas and Volume of a Sphere

Chapter 22: Tabular Representation of Statistical Data

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Measures of Central Tendency

Chapter 25: Probability

## Chapter 1: Number Systems

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.1 [Page 5]

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

Find five rational numbers between 1 and 2.

Find six rational numbers between 3 and 4.

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

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

Every whole number is a natural number.

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

Every integer is a rational number.

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

Every rational number is an integer.

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

Every natural number is a whole number.

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

Every integer is a whole number.

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

Every rational number is a whole number.

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.2 [Page 13]

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`

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?

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.3 [Page 22]

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

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

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

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

7.010

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

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

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

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

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

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

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

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

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

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.4 [Pages 31 - 32]

Define an irrational number ?

Explain, how irrational numbers differ from rational numbers ?

Examine, whether the following number are rational or irrational:

`sqrt7`

Examine, whether the following number are rational or irrational:

`sqrt4`

Examine, whether the following number are rational or irrational:

`2+sqrt3`

Examine, whether the following number are rational or irrational:

`sqrt3+sqrt2`

Examine, whether the following number are rational or irrational:

`sqrt3+sqrt5`

Examine, whether the following number are rational or irrational:

`(sqrt2-2)^2`

Examine, whether the following number are rational or irrational:

`(2-sqrt2)(2+sqrt2)`

Examine, whether the following number are rational or irrational:

`(sqrt2+sqrt3)^2`

Examine, whether the following number are rational or irrational:

`sqrt5-2`

Classify the following number as rational or irrational :-

`sqrt23`

Classify the following number as rational or irrational :-

`sqrt225`

Classify the following number as rational or irrational :-

0.3796

Classify the following number as rational or irrational :-

7.478478...

Classify the following number as rational or irrational :-

1.1010010001...

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

`sqrt4`

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

`3sqrt18`

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

`sqrt1.44`

`sqrt(9/27)`

`-sqrt64`

`sqrt100`

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

x^{2} = 5

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

y^{2} = 9

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

z^{2} = 0.04

*x, y, z* etc. represent rational or irrational number:

`u^2=17/4`

*x, y, z* etc. represent rational or irrational number:

v^{2} = 3

*x, y, z* etc. represent rational or irrational number:

w^{2} = 27

*x, y, z* etc. represent rational or irrational number:

t^{2} = 0.4

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

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

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

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

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

Give an example of two irrational numbers whose:

difference is a rational number.

Give an example of two irrational numbers whose:

difference is an irrational number.

Give an example of two irrational numbers whose:

sum is a rational number.

Give an example of two irrational numbers whose:

sum is an irrational number.

Give an example of two irrational numbers whose:

product is an rational number.

Give an example of two irrational numbers whose:

product is an irrational number.

Give an example of two irrational numbers whose:

quotient is a rational number.

Give an example of two irrational numbers whose:

quotient is an irrational number.

Find two irrational numbers between 0.5 and 0.55.

Find two irrational numbers lying between 0.1 and 0.12.

Prove that `sqrt3+sqrt5` is an irrational number.

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.5 [Page 36]

Complete the following sentence:

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

Complete the following sentence:

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

Complete the following sentence:

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

Complete the following sentence:

Every real number is either ______ number or _______ number.

Find whether the following statement is true or false.

Every real number is either rational or irrational.

Find whether the following statement is true or false.

π is an irrational number.

Find whether the following statement is true or false.

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

Represent `sqrt6,` `sqrt7,` `sqrt8` on the number line.

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

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.6 [Page 40]

Visualise 2.665 on the number line, using successive magnification.

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

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.7 [Pages 40 - 42]

Mark the correct alternative in the following:

Which one of the following is a correct statement?

Decimal expansion of a rational number is terminating

Decimal expansion of a rational number is non-terminating

Decimal expansion of an irrational number is terminating

Decimal expansion of an irrational number is non-terminating and non-repeating

Which one of the following statements is true?

The sum of two irrational numbers is always an irrational number

The sum of two irrational numbers is always a rational number

The sum of two irrational numbers may be a rational number or an irrational number

The sum of two irrational numbers is always an integer

Which of the following is a correct statement?

Sum of two irrational numbers is always irrational

Sum of a rational and irrational number is always an irrational number

Square of an irrational number is always a rational number

Sum of two rational numbers can never be an integer

Which of the following statements is true?

Product of two irrational numbers is always irrational

Product of a rational and an irrational number is always irrational

Sum of two irrational numbers can never be irrational

Sum of an integer and a rational number can never be an integer

Which of the following is irrational?

\[\sqrt{\frac{4}{9}}\]

\[\sqrt{\frac{4}{5}}\]

\[\sqrt{7}\]

\[\sqrt{81}\]

Which of the following is irrational?

0.14

`0.14overline16`

`0.overline1416`

0.1014001400014...

Which of the following is rational?

\[\sqrt{3}\]

\[\pi\]

\[\frac{4}{0}\]

\[\frac{0}{4}\]

The number 0.318564318564318564 ........ is:

a natural number

an integer

a rational number

an irrational number 0.318564318564318564.....` = 0overline318564` is repeating, so it is rational number because rational number is always either terminating or repeating.

If n is a natural number, then \[\sqrt{n}\] is

always a natural number

always an irrational number

always an irrational number

sometimes a natural number and sometimes an irrational number

Which of the following numbers can be represented as non-terminating, repeating decimals?

\[\frac{39}{24}\]

\[\frac{3}{16}\]

\[\frac{3}{11}\]

\[\frac{137}{25}\]

Every point on a number line represents

a unique real number

a natural number

a rational number

an irrational number

Which of the following is irrational?

0.15

0.01516

`0.overline1516`

0.5015001500015.

The number \[1 . \bar{{27}}\] in the form \[\frac{p}{q}\] , where p and q are integers and q ≠ 0, is

\[\frac{14}{9}\]

\[\frac{14}{11}\]

\[\frac{14}{13}\]

\[\frac{14}{15}\]

The number \[0 . \bar{3}\] in the form \[\frac{p}{q}\],where p and q are integers and q ≠ 0, is

\[\frac{33}{100}\]

\[\frac{3}{10}\]

\[\frac{1}{3}\]

\[\frac{3}{100}\]

\[0 . 3 \bar{2}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers q ≠ 0), is

\[\frac{8}{25}\]

\[\frac{29}{90}\]

\[\frac{32}{99}\]

\[\frac{32}{199}\]

\[23 . \bar{{43}}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers q ≠ 0), is

\[\frac{2320}{99}\]

\[\frac{2343}{100}\]

\[\frac{2343}{999}\]

\[\frac{2320}{199}\]

\[0 . \bar{{001}}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers, q ≠ 0), is

\[\frac{1}{1000}\]

\[\frac{1}{100}\]

\[\frac{1}{1999}\]

\[\frac{1}{999}\]

`"The value of "0.overline23 0.overline22 "is" `

`0.overline45`

`0.overline43`

`0.overline45`

`0.45`

An irrational number between 2 and 2.5 is

\[\sqrt{11}\]

\[\sqrt{5}\]

\[\sqrt{22 . 5}\]

\[\sqrt{12 . 5}\]

The number of consecutive zeros in \[2^3 \times 3^4 \times 5^4 \times 7\] is

3

2

4

5

The smallest rational number by which`1/3`should be multiplied so that its decimal expansion terminates after one place of decimal, is

\[\frac{1}{10}\]

\[\frac{3}{10}\]

3

30

### RD Sharma solutions for Mathematics for Class 9 Chapter 1 Number Systems Exercise 1.8 [Page 15]

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

## Chapter 1: Number Systems

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

RD Sharma solutions for Mathematics for Class 9 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 solutions in a manner that help students grasp basic concepts better and faster.

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