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In the decimal expansion of 23912/33333

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Retired Moderator
Joined: 12 Aug 2015
Posts: 2344
GRE 1: 323 Q169 V154
In the decimal expansion of 23912/33333 [#permalink]

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07 Nov 2016, 11:16
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37% (02:01) correct 63% (01:58) wrong based on 43 sessions

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In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7
[Reveal] Spoiler: OA

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Re: In the decimal expansion of 23912/33333 [#permalink]

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07 Nov 2016, 12:18
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stonecold wrote:
In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7

$$\frac{23912}{33333}$$ = 0.71736

There is a pattern , the set of 5 digits keeps repeating , so we have a cyclic order....

98/5 = 19 complete cycles and 3 remainder...

3rd digit from the right will be 7

Hence, the correct answer will be (E) 7

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Retired Moderator
Joined: 12 Aug 2015
Posts: 2344
GRE 1: 323 Q169 V154
In the decimal expansion of 23912/33333 [#permalink]

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07 Nov 2016, 12:29
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Abhishek009 wrote:
stonecold wrote:
In the decimal expansion of 23912/33333 ,what is the 98th digit to the right of the decimal.
A) 1
B) 2
C) 3
4) 6
5) 7

$$\frac{23912}{33333}$$ = 0.71736

There is a pattern , the set of 5 digits keeps repeating , so we have a cyclic order....

98/5 = 19 complete cycles and 3 remainder...

3rd digit from the right will be 7

Hence, the correct answer will be (E) 7

Hi.
Did you perform the long division ?
Actually we don't need to perform the division.

Any number of the form P/Q where P and Q are positive integers with the same number of digits and Q=10n-1 will have the same repeating pattern as the numerator.

E.G=>
3/9= 0.33333...
83/99= 0.83838383...
356/999=0.356356356...
1234/9999=0.123412341234...
34569/99999=0.345693456934569...

Hence
23912/33333 = 71736/9999=> 0.71736717367173671736.....
Clearly the pattern repeats after every 5 digits
So the 98th digit is 7

Regards
Stone Cold
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Re: In the decimal expansion of 23912/33333 [#permalink]

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13 Nov 2017, 07:33
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Re: In the decimal expansion of 23912/33333   [#permalink] 13 Nov 2017, 07:33
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