# Rational and Irrational Numbers ICSE ML Aggarwal Class-9 Maths

**Rational and Irrational Numbers ICSE** ML Aggarwal Class-9 Maths Chapter-1. Step by Step Answer of Exercise-1.1, Exercise-1.2, Exercise-1.3, Exercise-1.4, Exercise-1.5, MCQ and Chapter-Test of **Rational and Irrational Numbers **for **ICSE** Class-9 Mathematics**.** So This post is the Solution of ML Aggarwal Chapter 1- **Rational and Irrational Numbers **for **ICSE** Maths Class-9**.** Understanding ML Aggarwal Solutions (APC) Avichal Publication Solutions of Chapter- 1 Rational and Irrational Numbers. Visit official website CISCE for detail information about ICSE Board Class-9.

## Rational and Irrational Numbers ICSE ML Aggarwal Class-9 Maths

**–: Select Topics :–**

**and Chapter-Test , **

Note:- Before viewing Solution of Chapter -1 **Rational and Irrational Numbers Class-9** of ML Aggarwal Solutions. Read the Chapter Carefully then solve all example given in Exercise-1.1, Exercise-1.2, Exercise-1.3, Exercise-1.4 and Exercise-1.5. The Chapter-1 **Rational and Irrational Numbers Class-9 **is Main Chapter in Class 9 Mathematics.

**Exercise-1.1 Rational and Irrational Numbers Class-9 ML Aggarwal Chapter-1**

#### Question 1

Insert a rational number between and 2/9 and 3/8 arrange In descending order

#### Answer 1

3/8 , 43/144, 2/9

#### Question 2

Insert two rational numbers between 1/3 and 1/4 and arrange in ascending order

#### Answer 2

#### Question 3

Insert two rational numbers between – 1/3 and – 1/2 and arrange in ascending order

#### Answer 3

#### Question 4

Insert three rational numbers between 1/3 and 4/5 , and arrange in descending order.

#### Answer 4

#### Question 5

Insert three rational numbers between 4 and 4.5.

#### Answer 5

#### Question 6

Find six rational numbers between 3 and 4.

#### Answer 6

#### Question 7

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

#### Answer 7

#### Question 8

Find ten rational numbers between -2/5 and 1/7.

#### Answer 8

#### Question 9

Find six rational numbers between 1/2 and 2/3 !

#### Answer 9

**Chapter-1 Rational and Irrational Numbers EXERCISE – 1.2** C**lass-9 ML Solutions **

#### Question 1

Prove that , √5 is an irrational number.

#### Answer 1

#### Question 2

Prove that ,√7 is an irrational number.

#### Answer 2

#### Question 3

Prove that √6 is an irrational number.

#### Answer 3

#### Question 4

Prove that 1/√11 is an irrational number.

#### Answer 4

#### Question 5

Prove that √2 is an irrational number. Hence show that 3 — √2 is an irrational

#### Answer 5

#### Question 6

Prove that ,√3 is an irrational number. Hence, show that 2/5×√3 is an irrational number.

#### Answer 6

#### Question 7

Prove that √5 is an irrational number. Hence, show that -3 + 2√5 is an irrational number.

#### Answer 7

#### Question 8

Prove that the following numbers are irrational:

(i) 5+ √2

(ii) 3-5√3

(iii) 2√3-7

(iv) √2+√5

#### Answer 8

**Rational and Irrational Numbers Chapter-2 EXERCISE – 1.3 Solutions of ML Aggarwal Class-9**

#### Question 1

Locate √10 and √17 on the amber line

#### Answer 1

#### Question 2

Write the decimal expansion of each of the following numbers and say what kind of

decimal expansion each has:

(i) 36/100

(ii) 39/8

(iii) 2/9

(iv) 2/11

(v) 3/13

(vi) 329/400

#### Answer 2

#### Question 3

Without actually performing the king division, State whether the following rational

numbers will hare a terminating decimal expansion or a non-terminating repeating

decimal expansion:

(i) 13/3125

(ii) 17/8

(iii) 23/210

(iv) 6/15

(v) 1258/625

(vi) 77/210

#### Answer 3

#### Question 4

Without actually performing the long division, find if 987/10500 will have terminating or non.terminating repeating decimal expansion. Give reasons for your answer.

#### Answer 4

#### Question 5

Write the decimal expansions of the following numbers which have terminating decimal expansions:

(i) 17/8

(ii) 13/3125

(iïi)7/80

(vi)6/15

(v) 2²×7/5^{4}

^{(vi) 237/150}

#### Answer 5

#### Question 6

Write the denominator of the rational number 257/5000 in the form 2^{m}x5^{n }where m, n are non-negative integers. Hence, write its decimal expansion on without actual division

#### Answer 6

#### Question 7

Write the decimal expansion of 1/7. Hence, write the decimal expression of ? 2/7, 3/7 ,4/7, 5/7 and 6/7.

#### Answer 7

#### Question 8

Express the following numbers in the form p/q ’ . where p and q are both integers and q≠0;

(i)0.¯ ‾3

(ii) 5.¯‾2

(iii) 0.404040…….

(iv) 0.4‾7

(v) 0.1‾34

(vi)0.‾001

#### Answer 8

#### Question 9

Classify the following numbers as rational or irrational:(i) √23………………..

#### Answer 9

#### Question 10

The following …..of q.

#### Answer 10

#### Question 11

Insert…..following.

#### Answer 11

#### Question 12

inser……..3.

#### Answer 12

#### Question 13

write………….7/11.

#### Answer 13

#### Question 14

find………………..√3 .

#### Answer 14

#### Question 15

find…………√15.

#### Answer 15

#### Question 16

insert…………………..√7.

#### Answer 16

#### Question 17

Insert…….√7.

#### Answer 17

**EXERCISE-1.4 Rational and Irrational Numbers Chapter-1 Class-9 ML Aggarwal Solutions**

#### Question 1

Simlify the following

(i)………

(ii)………

(iii)……

(iv)……

(v)………

(vi)…….

#### Answer 1

#### Question 2

Simlify the following

(i)………

(ii)………

(iii)……

(iv)……

(v)………

(vi)…….

#### Answer 2

#### Question 3

If…………of.

(i)………

(ii)………

#### Answer 3

#### Question 4

If…………of.

(i)………

(ii)………

#### Answer 4

#### Question 5

State…………decimal.

(i)………

(ii)………

#### Answer 5

#### Question 6

State……………………..decimal.

(i)………

(ii)………

(iii)……

(iv)…..

Answer 6

#### Question 7

State……..irrational.

(i)………

(ii)………

(iii)……

(iv)…..

(v)………

(vi)………

(vii)……

(vii)…..

#### Answer 7

#### Question 8

Prove…………irrational.

(i)………

(ii)………

(iii)……

Answer 8

#### Question 9

Find……………numbers.

(i)………

(ii)………

#### Answer 9

#### Question 10

Write………………order.

(i)………

(ii)………

Answer 10

#### Question 11

Write………………order.

(i)………

(ii)………

#### Answer 11

#### Question 12

Arrange………………order.

Answer 12

**ML Solutions of Rational and Irrational Numbers EXERCISE – 1.5 Chapter-1 Class-9**

#### Question 1

Rationalise……………following.

(i)………..

(ii)…………

(iii)…………

(iv)…………

(v)………..

(vi)…………

(vii)…………

(viii)…………

#### Answer 1

#### Question 2

Simplifying………………..denominator.

(i)………..

(ii)…………

(iii)…………

Answer 2

#### Question 3

simplify………………

#### Answer 3

#### Question 4

simplify………………

#### Answer 4

#### Question 5

given……………if

(i)…………….

(ii)…………..

(iii)………..

#### Answer 5

#### Question 6

if………….numbers.

#### Answer 6

#### Question 7

if……………..decimal

(i)…………..

(ii)…………

#### Answer 7

#### Question 8

if a=……………..

#### Answer 8

#### Question 9

if x=……………..

#### Answer 9

#### Question 10

if x=…………..

#### Answer 10

#### Question 11

if p………………….

(i)…………..

(ii)…………

Answer 11

#### Question 12

if x=…………….

#### Answer 12

**MULTIPLE CHOICE QUESTION Chapter-1 Rational and Irrational Numbers ICSE Class-9 ML Solutions**

#### Question 1

Choose the correct answer from the given four options (1 to 21):

1 Choose the correct statement:

(a) Reciprocal of every rational number is a rational number.

(b) The square roots of all positive integers are irrational numbers.

(c) The product of a rational and an irrational number is an irrational number.

(d) The difference of a rational number and an irrational number is an irrational

number.

#### Answer 1

#### Question 2

Every rational number is

(a) a natural number

(b) an integer

(c) a real number

(d) a whole number

#### Answer 2

#### Question 3

Between two rational numbers

(a) there is no rational number

(b) there is exactly one rational number

(c) there are infinitely many rational numbers

(d) there are only rational numbers and no irrational numbers

#### Answer 3

#### Question 4

Decimal representation of a rational number cannot be

(a) terminating

(c) non-terminating repeating

(b) non-terminating

(d) non-terminating non-repeating

#### Answer 4

#### Question 5

The product of any two irrational numbers is

(a) always an irrational number

(c) always an integer

(b) always a rational number

(d) sometimes rational, sometimes irrational

#### Answer 5

#### Question 6

The division of two irrational numbers is

(a) a rational number

(b) an irrational number

(c) either a rational number or an irrational number

(d) neither rational number nor irrational number

#### Answer 6

#### Question 7

Which of the following is an irrational number?….

#### Answer 7

#### Question 8

Which of the following numbers has terminating decimal representation?……….

#### Answer 8

#### Question 9

Which of the following is an irrational number?

(b) 0:1416

(a) 0-14

(c) 0 1416

(d)0.4014001400014….

#### Answer 9

#### Question 10

Which of the following numbers has non-terminating repeating decimal ……….

#### Answer 10

#### Question 11

A rational number between 2 and 3 is

#### Answer 11

#### Question 12

The decimal expansion of 2- V3 is

(a) terminating and non-repeating

(b) terminating and.

(d) non-terminating and,

#### Answer 12

#### Question 13

The decimal expansion of the rational number

(a) one decimal place

(c) three decimal places

………………..

#### Answer 13

#### Question 14

V10 x V15 is equal to……………..

#### Answer 14

#### Question 15

2…………………….to

#### Answer 15

#### Question 16

The value of V8 + VI8 is

#### Answer 16

#### Question 17

The number (2 – 3 )2 is

(b) an integer

(d) an irrational number

(a) a natural number

(c) a rational number

#### Answer 17

#### Question 18

If x is a positive rational number which is not a perfect square, then -5 Vx is

(a) a negative integer

(b) an integer

(d) an irrational number

(c) a rational number

#### Answer 18

#### Question 19

If x, y are both positive rational numbers, then (Vx+ y)(Vx-Jy) is

(a) a rational number

(c) neither rational nor irrational number

(4) both rational as well as irrational number

(b) an irrational number

#### Answer 19

#### Question 20

After rationalising the denominator of………….

#### Answer 20

#### Question 21

The number obtained on rationalising the denominator of

#### Answer 21

**Chapter Test of Rational and Irrational Numbers ICSE Class-9 ML Solutions Chapter-1**

#### Question 1

Without actual division, find whether the following rational numbers are termin…………

#### Answer 1

#### Question 2

Express the following recurring decimals as vulgar fractions:

#### Answer 2

#### Question 3

insert……………….order.

#### Answer 3

#### Question 4

Insert a rational number between…………..

#### Answer 4

#### Question 5

Prove that the reciprocal of an irrational number is irrational.

#### Answer 5

#### Question 6

Prove that the following numbers are irrational…………

#### Answer 6

#### Question 7

Prove that …3 is an irrational number. Hence show that ……

#### Answer 7

#### Question 8

Prove that the following numbers are irrational:

#### Answer 8

#### Question 9

Rationalise the denominator of the following:

#### Answer 9

#### Question 10

If p,q are rational numbers and p – V15 a = 23- 5 find the values of p and q

#### Answer 10

#### Question 11

If x = ………………..

#### Answer 1

#### Question 12

(i) If x = ………………..

(ii) If x = ………………..

(iii) If x = ………………..

#### Answer 12

#### Question 13

Write the following real numbers in descending order:

#### Answer 13

#### Question 14

Find a rationral number and an irrational number between v3 and v5

#### Answer 14

#### Question 15

insert three irrational numbers between 2/3 and 25, and arrange in descending order.

#### Answer 15

#### Question 16

Give an example each of two different irrational numbers, whose

(i) sum is an irrational number.

(ii) product is an irrational number.

is a rational

#### Answer 16

#### Question 17

Give an example of two different irrational numbers, a and b, where a/b

is an irrational number.

#### Answer 17

#### Question 18

If 34:0356 is expressed in the form P, where p and g are coprime integers, then whát can you say about the factorisation of q?

#### Answer 18

#### Question 19

In each case, state whether the following numbers are rational or irrational. If they are

rational and expressed in the form 2, where p and g are coprime integers, then what

can you say about the prime factors of q?

(i) 279-034

(ii) 76-17893

(iii) 3.01001000

(iv) 39-546782

(v) 2.3476817681……

(vi) 59-120120012000…

#### Answer 19

**Return to ML Aggarawal Maths Solutions for ICSE Class-9.**

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