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Which of the following is the value of $0.142857142857 …$ in the form of $p q,$ where p and q are integers?

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17

110

14

611

answer is A.

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Detailed Solution

The given number is

0.142857142857 …

Let’s assume that the number be

x .

∴ x = 0.142857142857 … (1)

By multiplying both sides of the equation (1) by 10,00,000, we obtain,

1000000 x = 142857.142857... (2)

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

1000000 x − x = 142857.142857... − 0.142857...

⇒ 999999 x = 142857

⇒ x = 142857999999

∴ x = 17

Therefore, the number

0.142857142857 …

in the form

p q

is equal to

17 .

Hence, option (1) is correct.

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