# 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 1000.39 = 39/100

(ii)Multiplying and Dividing the number by 10000.750 = 750/1000 = 3/4

(iii)Multiplying and Dividing the number by 1002.15 = 215/100 = 43/20

(iv)Multiplying and Dividing the number by 10007.010 = 7010/1000 = 701/100

(v)Multiplying and Dividing the number by 1009.90 = 990/100 = 99/10

(vi)Multiplying and Dividing the number by 100001.0001 = 10001/10000

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

**Solution:**

(i)Let x = 0.4̅or x = 0.4̅ = 0.444 …. (1)

Multiplying both sides by 10

10x = 4.444 …..(2)

Subtract (1) by (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)

Subtract (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)

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

100x – 10x = 47.7777…. – 4.7777…

90x = 43

x = 43/90