Q.3. Express the following in the form pq where p and q are integers and q ≠ 0.

(i) 0.6 (ii) 0.47 (iii) 0.001

Solution:

(i) 0.6 = 0.666...

Let x = 0.666... (1)

⇒ 10x = 6.666... (2)

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

9x = 6

x = 23

(ii) 0.47= 0.4777...

Let x = 0.4777… (1)

⇒ 10x = 4.777… (2)

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

9x = 4.3

x = 4.39 = 4390

(iii) 0.001= 0.001001...

Let x = 0.001001... (1)

⇒ 1000x = 1.001001… (2)

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

999x = 1

x =1999