RD Sharma Solutions for Class 9 Mathematics Chapter 1 Exercise 1.5 Number System are provided here. This exercise helps students to understand and practise irrational numbers and the representation of real numbers and irrational numbers on the number line. RD Sharma Solutions for Class 9 Chapter 1 are designed by subject experts in accordance with the CBSE syllabus for Class 9.
RD Sharma Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.5
Access Answers to RD Sharma Solutions for Class 9 Chapter 1 Number System Exercise 1.5
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.
Draw on the number line:
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 centre, draw a semicircle, passing through A and C.
Step 5: Draw a line passing through B perpendicular to OB, and cut the semicircle at D.
Step 6: Consider B as a centre and BD as the radius draw an arc, cutting OC produced at E.
Now, from the 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 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 6 mentioned above, we will 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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