3 Express the following in the form p/q , where p and q are integers and q ≠0.

Question 3  Express the following in the form p/q , where p and q are integers and q ≠0.
 
Solution: (i)
Let x = 0.666…
Multiply by 10 we get 
10x = 6.666…
x = 0.666…
subtract them we get

9x  = 6 + x
9x = 6
Divide by 9 
x=6/9
simplify it by divide 3 we get 
x = 2/3 Answer

(ii)  
Let x = 0.4777…
Multiply by 10 we get 
10x = 4.7777…
x    = 0.4777…
subtract x we get 
9x  = 4.3
Divide by 9

X = 4.3/9 
To remove decimal add zero in denominator we get 
x = 43/90

(iii)  
Let x = 0.001001…
There are 3 repeating digits so multiply by 10*10*10 = 1000  
1000x = 1.001001…
X         = 0.001001…
subtract x there we get 
999 x   = 1 
Divide by 999 we get 
X = 1/999