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Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board chapter 2 - Real Numbers [Latest edition]

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Chapters

    1: Set Language

▶ 2: Real Numbers

    3: Algebra

    4: Geometry

    5: Coordinate Geometry

    6: Trigonometry

    7: Mensuration

    8: Statistics

    9: Probability

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board chapter 2 - Real Numbers - Shaalaa.com

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Solutions for Chapter 2: Real Numbers

Below listed, you can find solutions for Chapter 2 of Tamil Nadu Board of Secondary Education Samacheer Kalvi for Mathematics [English] Class 9 TN Board.

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.8Exercise 2.9

Exercise 2.1 [Page 45]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.1 [Page 45]

Exercise 2.1 | Q 1 | Page 45

Which arrow best shows the position of `11/3` on the number line?

Exercise 2.1 | Q 2 | Page 45

Find any three rational numbers between `(-7)/11` and `2/11`

Exercise 2.1 | Q 3. (i) | Page 45

Find any five rational numbers between `1/4` and `1/5`

Exercise 2.1 | Q 3. (ii) | Page 45

Find any five rational numbers between 0.1 and 0.11

Exercise 2.1 | Q 3. (iii) | Page 45

Find any five rational numbers between – 1 and – 2

Exercise 2.2 [Pages 51 - 52]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.2 [Pages 51 - 52]

Exercise 2.2 | Q 1. (i) | Page 51

Express the following rational numbers into decimal and state the kind of decimal expansion

`2/7`

Exercise 2.2 | Q 1. (ii) | Page 51

Express the following rational numbers into decimal and state the kind of decimal expansion

`-5 3/11`

Exercise 2.2 | Q 1. (iii) | Page 51

Express the following rational numbers into decimal and state the kind of decimal expansion

`22/3`

Exercise 2.2 | Q 1. (iv) | Page 51

Express the following rational numbers into decimal and state the kind of decimal expansion

`327/200`

Exercise 2.2 | Q 2 | Page 51

Express `1/13` in decimal form. Find the length of the period of decimal

Exercise 2.2 | Q 3 | Page 52

Express the rational number `1/33` in recurring decimal form by using the recurring decimal expansion of `1/11`. Hence write `71/33` in recurring decimal form.

Exercise 2.2 | Q 4. (i) | Page 52

Express the following decimal expression into rational number

`0. bar(24)`

Exercise 2.2 | Q 4. (ii) | Page 52

Express the following decimal expression into rational number

`2. bar(327)`

Exercise 2.2 | Q 4. (iii) | Page 52

Express the following decimal expression into rational number

– 5.132

Exercise 2.2 | Q 4. (iv) | Page 52

Express the following decimal expression into rational number

`3.1bar(7)`

Exercise 2.2 | Q 4. (v) | Page 52

Express the following decimal expression into rational number

`17. 2bar(15)`

Exercise 2.2 | Q 4. (vi) | Page 52

Express the following decimal expression into rational number

`-21.213bar(7)`

Exercise 2.2 | Q 5. (i) | Page 52

Without actual division, find the following rational numbers have terminating decimal expansion

`7/128`

Exercise 2.2 | Q 5. (ii) | Page 52

Without actual division, find the following rational numbers have terminating decimal expansion

`21/15`

Exercise 2.2 | Q 5. (iii) | Page 52

Without actual division, find the following rational numbers have terminating decimal expansion

`4 9/35`

Exercise 2.2 | Q 5. (iv) | Page 52

Without actual division, find the following rational numbers have terminating decimal expansion

`219/2200`

Exercise 2.3 [Page 55]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.3 [Page 55]

Exercise 2.3 | Q 1. (i) | Page 55

Represent the following irrational number on the number line

`sqrt(3)`

Exercise 2.3 | Q 1. (ii) | Page 55

Represent the following irrational number on the number line

`sqrt(4.7)`

Exercise 2.3 | Q 1. (iii) | Page 55

Represent the following irrational number on the number line

`sqrt(6.5)`

Exercise 2.3 | Q 2. (i) | Page 55

Find any two irrational numbers between 0.3010011000111…. and 0.3020020002….

Exercise 2.3 | Q 2. (ii) | Page 55

Find any two irrational numbers between `6/7` and `12/13`

Exercise 2.3 | Q 2. (iii) | Page 55

Find any two irrational numbers between `sqrt(2)` and `sqrt(3)`

Exercise 2.3 | Q 3 | Page 55

Find any two rational numbers between 2.2360679……… and 2.236505500……….

Exercise 2.4 [Page 57]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.4 [Page 57]

Exercise 2.4 | Q 1. (i) | Page 57

Represent the following numbers on the number line

5.348

Exercise 2.4 | Q 1. (ii) | Page 57

Represent the following numbers on the number line

`6.bar(4)` upto 3 decimal places

Exercise 2.4 | Q 1. (iii) | Page 57

Represent the following numbers on the number line

`4.bar(73)` upto 4 decimal places

Exercise 2.5 [Pages 59 - 60]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.5 [Pages 59 - 60]

Exercise 2.5 | Q 1. (i) | Page 59

Write the following in the form of 5ⁿ:

625

Exercise 2.5 | Q 1. (ii) | Page 59

Write the following in the form of 5ⁿ:

`1/5`

Exercise 2.5 | Q 1. (iii) | Page 59

Write the following in the form of 5ⁿ:

`sqrt(5)`

Exercise 2.5 | Q 1. (iv) | Page 59

Write the following in the form of 5ⁿ:

`sqrt(125)`

Exercise 2.5 | Q 2. (i) | Page 59

Write the following in the form of 4ⁿ:

16

Exercise 2.5 | Q 2. (ii) | Page 59

Write the following in the form of 4ⁿ:

8

Exercise 2.5 | Q 2. (iii) | Page 59

Write the following in the form of 4ⁿ:

32

Exercise 2.5 | Q 3. (i) | Page 59

Find the value of `(49)^(1/2)`

Exercise 2.5 | Q 3. (ii) | Page 59

Find the value of `(243)^(2/5)`

Exercise 2.5 | Q 3. (iii) | Page 59

Find the value of `9^((-3)/2)`

Exercise 2.5 | Q 3. (iv) | Page 59

Find the value of `(64/125)^((-2)/3)`

Exercise 2.5 | Q 4. (i) | Page 59

Use a fractional index to write: `sqrt(5)`

Exercise 2.5 | Q 4. (ii) | Page 59

Use a fractional index to write: `root(2)(7)`

Exercise 2.5 | Q 4. (iii) | Page 59

Use a fractional index to write: `(root(3)(49))^5`

Exercise 2.5 | Q 4. (iv) | Page 59

Use a fractional index to write: `(1/root(3)(100))^7`

Exercise 2.5 | Q 5. (i) | Page 60

Find the 5^th root of 32

Exercise 2.5 | Q 5. (ii) | Page 60

Find the 5^th root of 243

Exercise 2.5 | Q 5. (iii) | Page 60

Find the 5^th root of 100000

Exercise 2.5 | Q 5. (iv) | Page 60

Find the 5^th root of `1024/3125`

Exercise 2.6 [Page 68]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.6 [Page 68]

Exercise 2.6 | Q 1. (i) | Page 68

Simplify the following using addition and subtraction properties of surds:

`5sqrt(3) + 18sqrt(3) - 2sqrt(3)`

Exercise 2.6 | Q 1. (ii) | Page 68

Simplify the following using addition and subtraction properties of surds:

`4root(3)(5) + 2root(3)(5) - 3root(3)(5)`

Exercise 2.6 | Q 1. (iii) | Page 68

Simplify the following using addition and subtraction properties of surds:

`3sqrt(75) + 5sqrt(48) - sqrt(243)`

Exercise 2.6 | Q 1. (iv) | Page 68

Simplify the following using addition and subtraction properties of surds:

`5root(3)(40) + 2root(3)(625) - 3root(3)(320)`

Exercise 2.6 | Q 2. (i) | Page 68

Simplify the following using multiplication and division properties of surds:

`sqrt(3) xx sqrt(5) xx sqrt(2)`

Exercise 2.6 | Q 2. (ii) | Page 68

Simplify the following using multiplication and division properties of surds:

`sqrt(35) ÷ sqrt(7)`

Exercise 2.6 | Q 2. (iii) | Page 68

Simplify the following using multiplication and division properties of surds:

`root(3)(27) xx root(3)(8) xx root(3)(125)`

Exercise 2.6 | Q 2. (iv) | Page 68

Simplify the following using multiplication and division properties of surds:

`(7sqrt("a") - 5sqrt("b")) (7sqrt("a") + 5sqrt("b"))`

Exercise 2.6 | Q 2. (v) | Page 68

Simplify the following using multiplication and division properties of surds:

`[sqrt(225/729) - sqrt(25/144)] ÷ sqrt(16/81)`

Exercise 2.6 | Q 3. (i) | Page 68

If `sqrt(2)` = 1.414, `sqrt(3)` = 1.732, `sqrt(5)` = 2.236, `sqrt(10)` = 3.162, then find the values of the following correct to 3 places of decimals.

`sqrt(40) - sqrt(20)`

Exercise 2.6 | Q 3. (ii) | Page 68

If `sqrt(2)` = 1.414, `sqrt(3)` = 1.732, `sqrt(5)` = 2.236, `sqrt(10)` = 3.162, then find the values of the following correct to 3 places of decimals.

`sqrt(300) + sqrt(90) - sqrt(8)`

Exercise 2.6 | Q 4. (i) | Page 68

Arrange surds in descending order:

`root(3)(5), root(9)(4), root(6)(3)`

Exercise 2.6 | Q 4. (ii) | Page 68

Arrange surds in descending order:

`root(2)root(3)(5), root(3)root(4)(7), sqrt(sqrt(3)`

Exercise 2.6 | Q 5. (i) | Page 68

Can you get a pure surd when you find the sum of two surds Justify answer with an example

Exercise 2.6 | Q 5. (ii) | Page 68

Can you get a pure surd when you find the difference of two surds Justify answer with an example

Exercise 2.6 | Q 5. (iii) | Page 68

Can you get a pure surd when you find the product of two surds Justify answer with an example.

Exercise 2.6 | Q 5. (iv) | Page 68

Can you get a pure surd when you find the quotient of two surds Justify answer with an example

Exercise 2.6 | Q 6. (i) | Page 68

Can you get a rational number when you compute the sum of two surds Justify answer with an example

Exercise 2.6 | Q 6. (ii) | Page 68

Can you get a rational number when you compute the difference of two surds Justify answer with an example

Exercise 2.6 | Q 6. (iii) | Page 68

Can you get a rational number when you compute the product of two surds Justify answer with an example

Exercise 2.6 | Q 6. (iv) | Page 68

Can you get a rational number when you compute the quotient of two surds Justify answer with an example

Exercise 2.7 [Page 70]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.7 [Page 70]

Exercise 2.7 | Q 1. (i) | Page 70

Rationalise the denominator `1/sqrt(50)`

Exercise 2.7 | Q 1. (ii) | Page 70

Rationalise the denominator `5/(3sqrt(5))`

Exercise 2.7 | Q 1. (iii) | Page 70

Rationalise the denominator `sqrt(75)/sqrt(18)`

Exercise 2.7 | Q 1. (iv) | Page 70

Rationalise the denominator `(3sqrt(5))/sqrt(6)`

Exercise 2.7 | Q 2. (i) | Page 70

Rationalise the denominator and simplify `(sqrt(48) + sqrt(32))/(sqrt(27) - sqrt(18))`

Exercise 2.7 | Q 2. (ii) | Page 70

Rationalise the denominator and simplify `(5sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`

Exercise 2.7 | Q 2. (iii) | Page 70

Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`

Exercise 2.7 | Q 2. (iv) | Page 70

Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`

Exercise 2.7 | Q 3 | Page 70

Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = "a"sqrt(7) + "b"`

Exercise 2.7 | Q 4 | Page 70

If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`

Exercise 2.7 | Q 5 | Page 70

Given `sqrt(2)` = 1.414, find the value of `(8 - 5sqrt(2))/(3 - 2sqrt(2))` (to 3 places of decimals).

Exercise 2.8 [Pages 73 - 74]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.8 [Pages 73 - 74]

Exercise 2.8 | Q 1. (i) | Page 73

Represent the following numbers in the scientific notation:

569430000000

Exercise 2.8 | Q 1. (ii) | Page 73

Represent the following numbers in the scientific notation:

2000.57

Exercise 2.8 | Q 1. (iii) | Page 73

Represent the following numbers in the scientific notation:

0.0000006000

Exercise 2.8 | Q 1. (iv) | Page 73

Represent the following number in the scientific notation:

0.0009000002

Exercise 2.8 | Q 2. (i) | Page 73

Write the following numbers in decimal form:

3.459 × 10⁶

Exercise 2.8 | Q 2. (ii) | Page 73

Write the following numbers in decimal form:

5.678 × 10⁴

Exercise 2.8 | Q 2. (III) | Page 73

Write the following numbers in decimal form:

1.00005 × 10⁻⁵

Exercise 2.8 | Q 2. (iv) | Page 73

Write the following numbers in decimal form:

2.530009 × 10⁻⁷

Exercise 2.8 | Q 3. (i) | Page 73

Represent the following numbers in scientific notation:

(300000)² × (20000)⁴

Exercise 2.8 | Q 3. (ii) | Page 73

Represent the following numbers in scientific notation:

(0.000001)¹¹÷ (0.005)³

Exercise 2.8 | Q 3. (iii) | Page 73

Represent the following numbers in scientific notation:

`{(0.00003)^6 xx (0.00005)^4} ÷ {(0.009)^3 xx (0.05)^2}`

Exercise 2.8 | Q 4. (i) | Page 74

Represent the following information in scientific notation:

The world population is nearly 7000,000,000

Exercise 2.8 | Q 4. (ii) | Page 74

Represent the following information in scientific notation:

One light year means the distance 9460528400000000 km

Exercise 2.8 | Q 4. (iii) | Page 74

Represent the following information in scientific notation:

Mass of an electron is 0.000 000 000 000 000 000 000 000 000 00091093822 kg

Exercise 2.8 | Q 5. (i) | Page 74

Simplify: (2.75 × 10⁷) + (1.23 × 10⁸)

Exercise 2.8 | Q 5. (ii) | Page 74

Simplify: (1.598 × 10¹⁷) – (4.58 × 10¹⁵)

Exercise 2.8 | Q 5. (iii) | Page 74

Simplify: (1.02 × 10¹⁰) × (1.20 × 10⁻³)

Exercise 2.8 | Q 5. (iv) | Page 74

Simplify: (8.41 × 10⁴) ÷ (4.3 × 10⁵)

Exercise 2.9 [Pages 74 - 76]

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board 2 Real Numbers Exercise 2.9 [Pages 74 - 76]

Multiple Choice Questions

Exercise 2.9 | Q 1 | Page 74

If n is a natural number then `sqrt("n")` is

always a natural number.
always an irrational number.
always a rational number
may be rational or irrational

Exercise 2.9 | Q 2 | Page 74

Which of the following is not true?

Every rational number is a real number
Every integer is a rational number
Every real number is an irrational number
Every natural number is a whole number

Exercise 2.9 | Q 3 | Page 74

Which one of the following, regarding sum of two irrational numbers, is true?

always an irrational number
may be a rational or irrational number
always a rational number
always an integer

Exercise 2.9 | Q 4 | Page 74

Which one of the following has a terminating decimal expansion?

`5/64`
`8/9`
`14/15`
`1/12`

Exercise 2.9 | Q 5 | Page 75

Which one of the following is an irrational number

`sqrt(25)`
`sqrt(9/4)`
`7/11`
π

Exercise 2.9 | Q 6 | Page 75

An irrational number between 2 and 2.5 is

`sqrt(11)`
`sqrt(5)`
`sqrt(2.5)`
`sqrt(8)`

Exercise 2.9 | Q 7 | Page 75

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

`1/10`
`3/10`
3
30

Exercise 2.9 | Q 8 | Page 75

If `1/7 = 0.bar(142857)` then the value of `5/7` is

`0.bar(142857)`
`0.bar(714285)`
`0.bar(571428)`
0.714285

Exercise 2.9 | Q 9 | Page 75

Find the odd one out of the following.

`sqrt(32) xx sqrt(2)`
`sqrt(27)/sqrt(3)`
`sqrt(72) xx sqrt(8)`
`sqrt(54)/sqrt(18)`

Exercise 2.9 | Q 10 | Page 75

`0.bar(34) + 0.3bar(4)` =

`0.6bar(87)`
`0.bar(68)`
`0.6bar(8)`
`0.68bar(7)`

Exercise 2.9 | Q 11 | Page 75

Which of the following statement is false?

The square root of 25 is 5 or −5
`-sqrt(25)` = −5
`sqrt(25)` = 5
`sqrt(25)` = ± 5

Exercise 2.9 | Q 12 | Page 75

Which one of the following is not a rational number?

`sqrt(8/18)`
`7/3`
`sqrt(0.01)`
`sqrt(13)`

Exercise 2.9 | Q 13 | Page 75

`sqrt(27) + sqrt(12)` =

`sqrt(39)`
`5sqrt(6)`
`5sqrt(3)`
`3sqrt(5)`

Exercise 2.9 | Q 14 | Page 75

If `sqrt(80) = "k"sqrt(5)`, then k =

2
4
8
16

Exercise 2.9 | Q 15 | Page 75

`4sqrt(7) xx 2sqrt(3)` =

`6sqrt(10)`
`8sqrt(21)`
`8sqrt(10)`
`6sqrt(21)`

Exercise 2.9 | Q 16 | Page 75

When written with a rational denominator, the expression `(2sqrt(3))/(3sqrt(2))` can be simplified as

`sqrt(2)/3`
`sqrt(3)/2`
`sqrt(6)/3`
`2/3`

Exercise 2.9 | Q 17 | Page 76

When `(2sqrt(5) - sqrt(2))^2` is simplified, we get

`4sqrt(5) + 2sqrt(2)`
`22 - 4sqrt(10)`
`8 - 4sqrt(10)`
`2sqrt(10) - 2`

Exercise 2.9 | Q 18 | Page 76

`(0.000729)^((-3)/4) xx (0.09)^((-3)/4)` = ______

`(10^3)/(3^3)`
`(10^5)/(3^5)`
`(10^2)/(3^2)`
`(10^6)/(3^6)`

Exercise 2.9 | Q 19 | Page 76

If `sqrt(9^x) = root(3)(9^2)`, then x = ______

`2/3`
`4/3`
`1/3`
`5/3`

Exercise 2.9 | Q 20 | Page 76

The length and breadth of a rectangular plot are 5 × 10⁵ and 4 × 10⁴ metres respectively. Its area is ______

9 × 10¹ m²
9 × 10⁹ m²
2 × 10¹⁰m²
20 × 10²⁰ m²

Solutions for 2: Real Numbers

Exercise 2.1Exercise 2.2Exercise 2.3Exercise 2.4Exercise 2.5Exercise 2.6Exercise 2.7Exercise 2.8Exercise 2.9

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board chapter 2 - Real Numbers - Shaalaa.com

Samacheer Kalvi solutions for Mathematics [English] Class 9 TN Board chapter 2 - Real Numbers

Shaalaa.com has the Tamil Nadu Board of Secondary Education Mathematics Mathematics [English] Class 9 TN Board Tamil Nadu Board of Secondary Education solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Samacheer Kalvi solutions for Mathematics Mathematics [English] Class 9 TN Board Tamil Nadu Board of Secondary Education 2 (Real Numbers) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Samacheer Kalvi textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics [English] Class 9 TN Board chapter 2 Real Numbers are Rational Numbers, Denseness Property of Rational Numbers, Concept of Irrational Numbers, Representation of Irrational Numbers on the Number Line, Decimal Representation of Rational Numbers, Period of Decimal, Conversion of Terminating Decimals into Rational Numbers, Conversion of Non-terminating and Recurring Decimals into Rational Numbers, Decimal Representation to Identify Irrational Numbers, Concept of Real Numbers, Representing Real Numbers on the Number Line, Radical Notation, Fractional Index, Surds, Order of a Surd, Laws of Radicals, Operations on Surds, Rationalisation of Surds, Scientific Notation, Converting Scientific Notation to Decimal Form, Arithmetic of Numbers in Scientific Notation.

Using Samacheer Kalvi Mathematics [English] Class 9 TN Board solutions Real Numbers exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in Samacheer Kalvi Solutions are essential questions that can be asked in the final exam. Maximum Tamil Nadu Board of Secondary Education Mathematics [English] Class 9 TN Board students prefer Samacheer Kalvi Textbook Solutions to score more in exams.

Get the free view of Chapter 2, Real Numbers Mathematics [English] Class 9 TN Board additional questions for Mathematics Mathematics [English] Class 9 TN Board Tamil Nadu Board of Secondary Education, and you can use Shaalaa.com to keep it handy for your exam preparation.

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