RD Sharma Solutions for Class 9 Mathematics Chapter 1 Exercise 1.3 Number System is provided here. The RD Sharma Solutions for Class 9 Chapter 1 textbook questions will help students to understand the concepts and to practise higher-level questions related to the number system. This exercise is based on the conversion of decimal numbers into rational numbers. Click on the link below to download the free PDFs of RD Sharma Solutions for Class 9 Chapter 1.
RD Sharma Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.3
Access Answers to RD Sharma Solutions for Class 9 Maths Chapter 1 Number System Exercise 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
RD Sharma Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.3
RD Sharma Solutions for Class 9 Maths Chapter 1 Number System Exercise 1.3 is based on the following topics and subtopics:
- Conversion of decimal numbers into rational numbers of the form m/n
- Conversion of terminating decimal number to the form p/q
- Conversion of a pure recurring decimal to the form p/q
- Conversion of a mixed recurring decimal to the form p/q
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