Class 9 RD Sharma Solutions - 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) Multiplying and Dividing the number by 100

0.39 = 39/100

(ii) Multiplying and Dividing the number by 1000

0.750 = 750/1000 = 3/4

(iii) Multiplying and Dividing the number by 100

2.15 = 215/100 = 43/20

(iv) Multiplying and Dividing the number by 1000

7.010 = 7010/1000 = 701/100

(v) Multiplying and Dividing the number by 100

9.90 = 990/100 = 99/10

(vi) Multiplying and Dividing the number by 10000

1.0001 = 10001/10000

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

\\(i)\hspace{0.5mm}0.\overline{4}\hspace{1cm}(ii)0.\overline{37}\\ (iii)\hspace{0.5mm}0.\overline{54}\hspace{1cm}(iv)0.\overline{621}\\ (v)\hspace{0.5mm}125.\overline{3}\hspace{1cm}(vi)4.\overline{7}\\ (vii)\hspace{0.5mm}0.\overline{47}

Solution:

(i) Let x = 0.4̅

or x = 0.4̅ = 0.444 …. (1)

Multiplying both sides by 10

10x = 4.444 …..(2)

Subtracting (1) from (2), 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)

Subtracting (1) from (2), 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)

Subtracting (1) from (2), we get

100x – x = 54.5454…. – 0.5454….

99x = 54

x = 54/99

= 18 / 33

(iv) Let x = 0.621621… (1)

Multiplying both sides by 1000

1000x = 621.621621…. (2)

Subtracting (1) from (2), 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)

Subtracting (1) from (2), 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)

Subtracting (1) from (2), 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)

Subtracting (1) from (2), we get

100x – 10x = 47.7777…. – 4.7777…

90x = 43

x = 43/90