RD Sharma Class 9 Solutions Chapter 1 Exercise 1.3 (Updated for 2024)

RD Sharma Class 9 Solutions Chapter 1 Exercise 1.3: For scoring a good score it is important to do good preparation as well. For that, you can study RD Sharma Solutions Class 9 Maths. The RD Sharma Solutions for Class 9 Chapter 1 textbook questions will help students to understand the concepts and to practice higher-level questions related to the number system. This exercise is based on the conversion of decimal numbers into rational numbers. All the solutions are designed by subject matter experts and are very reliable. To know more about the RD Sharma Class 9 Solutions Chapter 1 Exercise 1.3, read the whole blog.

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RD Sharma Class 9 Solutions Chapter 1 Exercise 1.3

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RD Sharma Class 9 Solutions Chapter 1 Number System Ex 1.3

Question 1: Express each of the following decimals in the form p/q:

(i) 0.39

(ii) 0.750

(iii) 2.15

(iv) 7.010

(v) 9.90

(vi) 1.0001

Solution:

(i)

0.39 = 39/100

(ii)

0.750 = 750/1000 = 3/4

(iii)

2.15 = 215/100 = 43/20

(iv)

7.010 = 7010/1000 = 701/100

(v)

9.90 = 990/100 = 99/10

(vi)

1.0001 = 10001/10000

Question 2: Express each of the following decimals in the form p/q:

Solution:

(i) Let x = 0.4̅

or x = 0.4̅ = 0.444 …. (1)

Multiplying both sides by 10

10x = 4.444 …..(2)

Subtract (1) by (2), and we get

10x – x = 4.444… – 0.444…

9x = 4

x = 4/9

=> 0.4̅ = 4.9

(ii) Let x = 0.3737.. …. (1)

Multiplying both sides by 100

100x = 37.37… …..(2)

Subtract (1) from (2), and we get

100x – x = 37.37… – 0.3737…

100x – x = 37

99x = 37

x = 37/99

(iii) Let x = 0.5454… (1)

Multiplying both sides by 100

100x = 54.5454…. (2)

Subtract (1) from (2), and we get

100x – x = 54.5454…. – 0.5454….

99x = 54

x = 54/99

(iv) Let x = 0.621621… (1)

Multiplying both sides by 1000

1000x = 621.621621…. (2)

Subtract (1) from (2), and we get

1000x – x = 621.621621…. – 0.621621….

999x = 621

x = 621/999

or x = 23/37

(v) Let x = 125.3333…. (1)

Multiplying both sides by 10

10x = 1253.3333…. (2)

Subtract (1) from (2), and we get

10x – x = 1253.3333…. – 125.3333….

9x = 1128

or x = 1128/9

or x = 376/3

(vi) Let x = 4.7777…. (1)

Multiplying both sides by 10

10x = 47.7777…. (2)

Subtract (1) from (2), and we get

10x – x = 47.7777…. – 4.7777….

9x = 43

x = 43/9

(vii) Let x = 0.47777….

Multiplying both sides by 10

10x = 4.7777…. …(1)

Multiplying both sides by 100

100x = 47.7777…. (2)

Subtract (1) from (2), and we get

100x – 10x = 47.7777…. – 4.7777…

90x = 43

x = 43/90

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