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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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13

110

23

611

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

10 x = 6.666 … (2)

By subtracting equation (1) from equation (2), we obtain,

10 x − x = 6.6666 − 0.6666 ⇒ 9 x = 6

⇒ 9 x 9 = 69 ⇒ x = 23

Therefore, the number

0.6666...

in the form

p q

is equal to

23 .

Hence, option (3) is correct.

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