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Q.

Which of the following is the value of 0.6666…   in the form of p q ,  where p and q are integers?


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a

1 3  

b

1 10  

c

2 3  

d

6 11    

answer is C.

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Detailed Solution

The given number is 0.6666…  
Let’s assume that the number be x.   ∴x=0.6666…        (1)   By multiplying both sides of the equation (1) by 10, we obtain 10x=6.666…                   (2)  
By subtracting equation (1) from equation (2), we obtain,
10x−x=6.6666−0.6666 ⇒9x=6  
⇒ 9x 9 = 6 9 ⇒x= 2 3  
Therefore, the number 0.6666...   in the form p q   is equal to 2 3 .  
Hence, option (3) is correct.
 
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