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# Class 9 RD Sharma Solutions – Chapter 1 Number System – Exercise 1.3

• Last Updated : 02 Dec, 2020

### (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:

Solution:

(i) Let x = 0.4Ì…

or x = 0.4Ì… = 0.444 â€¦. (1)

Multiplying both sides by 10

10x = 4.444 â€¦..(2)

Subtract (1) by (2), we get

10x â€“ x = 4.444â€¦ â€“ 0.444â€¦

9x = 4

x = 4/9

=> 0.4Ì… = 4.9

(ii) Let x = 0.3737.. â€¦. (1)

Multiplying both sides by 100

100x = 37.37â€¦ â€¦..(2)

Subtract (1) from (2), we get

100x â€“ x = 37.37â€¦ â€“ 0.3737â€¦

100x â€“ x = 37

99x = 37

x = 37/99

(iii) Let x = 0.5454â€¦ (1)

Multiplying both sides by 100

100x = 54.5454â€¦. (2)

Subtract (1) from (2), we get

100x â€“ x = 54.5454â€¦. â€“ 0.5454â€¦.

99x = 54

x = 54/99

(iv) Let x = 0.621621â€¦ (1)

Multiplying both sides by 1000

1000x = 621.621621â€¦. (2)

Subtract (1) from (2), we get

1000x â€“ x = 621.621621â€¦. â€“ 0.621621â€¦.

999x = 621

x = 621/999

or x = 23/37

(v) Let x = 125.3333â€¦. (1)

Multiplying both sides by 10

10x = 1253.3333â€¦. (2)

Subtract (1) from (2), we get

10x â€“ x = 1253.3333â€¦. â€“ 125.3333â€¦.

9x = 1128

or x = 1128/9

or x = 376/3

(vi) Let x = 4.7777â€¦. (1)

Multiplying both sides by 10

10x = 47.7777â€¦. (2)

Subtract (1) from (2), we get

10x â€“ x = 47.7777â€¦. â€“ 4.7777â€¦.

9x = 43

x = 43/9

(vii) Let x = 0.47777â€¦.

Multiplying both sides by 10

10x = 4.7777â€¦. â€¦(1)

Multiplying both sides by 100

100x = 47.7777â€¦. (2)

Subtract (1) from (2), we get

100x â€“ 10x = 47.7777â€¦. â€“ 4.7777â€¦

90x = 43

x = 43/90

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