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 that 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 many 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 many 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 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.
Draw on number line:
Question 3: Represent √3.5, √9.4, √10.5 and on the real number line.
Solution:
Represent √3.5 on 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 centre draw a semi circle, passing through A and C.
Step 5: Draw a line passing through B perpendicular to OB, and cut semicircle at D.
Step 6: Consider B as a centre and BD as 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 number line
Step 1: Draw a line segment AB = 9.4 units
Follow step 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 number line
Step 1: Draw a line segment AB = 10.5 units
Follow step 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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