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By dividing 21 into 1, the fraction 1/21 can be written

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By dividing 21 into 1, the fraction 1/21 can be written [#permalink]

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New post 19 May 2017, 02:22
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By dividing 21 into 1, the fraction 1/21 can be written as a repeating decimal: 0.476190476190 . . . where the block of digits 476190 repeats. What is the 54th digit following the decimal point?

(A) 0
(B) 4
(C) 6
(D) 7
(E) 9

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Re: By dividing 21 into 1, the fraction 1/21 can be written [#permalink]

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New post 19 May 2017, 02:35
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6 digits(476190) repeats itself. Thus, the digits represent:
4 - (6n+1)th term
7 - (6n+2)th term
6 - (6n+3)th term
1 - (6n+4)th term
9 - (6n+5)th term
0 - (6n+6)th term
Now 54th = 8*6+6. Hence the 54th digit is 0.
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Re: By dividing 21 into 1, the fraction 1/21 can be written [#permalink]

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New post 19 May 2017, 03:09
So basically a 6-digit code is being repeated. We have to find which of the 6 digits will appear at the 54th place.

Clearly we can see that 54 is divisible by 6. This means digit will be the 6th (last one) of the code. Which is '0'.
Hence answer is A.
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Re: By dividing 21 into 1, the fraction 1/21 can be written [#permalink]

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New post 22 May 2017, 18:48
rohan2345 wrote:
By dividing 21 into 1, the fraction 1/21 can be written as a repeating decimal: 0.476190476190 . . . where the block of digits 476190 repeats. What is the 54th digit following the decimal point?

(A) 0
(B) 4
(C) 6
(D) 7
(E) 9


We see that we have a repeating pattern of 6 numbers in which 0 is the 6th digit. If we were to count out this pattern, we would discover that the 6th digit, the 12th digit, and the 18th digit would all be 0. In fact, the nth digit, where n is a multiple of 6, will always be 0. Since 54 is also a multiple of 6, the 54th digit will be 0.

Answer: A
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Re: By dividing 21 into 1, the fraction 1/21 can be written   [#permalink] 22 May 2017, 18:48
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