RD Sharma Class 9 Solutions Chapter 1 Exercise 1.5 (Updated for 2024)

RD Sharma Class 9 Solutions Chapter 1 Exercise 1.5: Complete the Class 9 Maths assignments or clear your exams with good marks with the RD Sharma Solutions Class 9 Maths. You can get reliable solutions from RD Sharma Class 9 Solutions Chapter 1 Exercise 1.5 as they are designed by subject matter experts. To know more, read the whole blog. 

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RD Sharma Class 9 Solutions Chapter 1 Exercise 1.5

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Question 1: Complete the following sentences:

(i) Every point on the number line corresponds to a …… number which may be either …… or …….

(ii) The decimal form of an irrational number is neither ….. nor ……

(iii) The decimal representation of a rational number is either ..… or …..

(iv) Every real number is either … number or … number.

Solution:

(i) Every point on the number line corresponds to a real number which may be either rational or irrational.

(ii) The decimal form of an irrational number is neither terminating nor repeating.

(iii) The decimal representation of a rational number is either terminating or non-terminating recurring.

(iv) Every real number is either a rational number or an irrational number.

Question 2: Represent √6, √7, √8 on the number line.

Solution:

Find the equivalent values of √6, √7, √8

√6 = 2.449

√7 = 2.645

√8 = 2.828

We can see that all the given numbers lie between 2 and 3.

Question 3: Represent √3.5, √9.4, √10.5 and on the real number line.

Solution:

Represent √3.5 on a number line

Step 1: Draw a line segment AB = 3.5 units

Step 2: Produce B till point C, such that BC = 1 unit

Step 3: Find the mid-point of AC, say O.

Step 4: Taking O as the center draw a semi-circle, passing through A and C.

Step 5: Draw a line passing through B perpendicular to OB, and cut a semicircle at D.

Step 6: Consider B as a center and BD as the radius draw an arc-cutting OC produced at E.

Now, from right triangle OBD,

BD² = OD² – OB²

= OC² – (OC – BC)²

(As, OD = OC)

BD² = 2OC x BC – (BC)²

= 2 x 2.25 x 1 – 1

= 3.5

=> BD = √3.5

Represent √9.4 on a number line

Step 1: Draw a line segment AB = 9.4 units

Follow steps 2 to Step 6 mentioned above.

BD² = 2OC x BC – (BC)²

= 2 x 5.2 x 1 – 1

= 9.4

=> BD = √9.4

Represent √10.5 on a number line

Step 1: Draw a line segment AB = 10.5 units

Following steps 2 to Step 6 mentioned above, we get

BD² = 2OC x BC – (BC)²

= 2 x 5.75 x 1 – 1

= 10.5

=> BD = √10.5

Question 4: Find whether the following statements are true or false:

(i) Every real number is either rational or irrational.

(ii) π is an irrational number.

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

Solution:

(i) True.

(ii) True.

(ii) False.

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