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# If each of the following fractions were written as a

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Senior Manager
Joined: 04 May 2005
Posts: 265
Location: CA, USA
If each of the following fractions were written as a  [#permalink]

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20 Sep 2005, 21:59
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If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits ?
A) 2/11
B) 1/3
C) 41/99
D) 2/3
E) 23/37
F) 1/7

(I added one more choice to the original question.)

Is there an easy way to get result without calculating each choice ?

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Manager
Joined: 19 Jul 2005
Posts: 52
Re: PS: OG11 No. 22 recurring decimals  [#permalink]

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20 Sep 2005, 22:21
qpoo wrote:
If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits ?
A) 2/11
B) 1/3
C) 41/99
D) 2/3
E) 23/37
F) 1/7

(I added one more choice to the original question.)

Is there an easy way to get result without calculating each choice ?

It should be 1/7 which is having a sequence 0.142857
Senior Manager
Joined: 27 Aug 2005
Posts: 328

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21 Sep 2005, 06:15
You can eliminate a couple of choices right off the bat before going to the step of calculating them out. For example, 1/3 is an obvious one to eliminate, because it is simply 0.3333333 and therefore would have the shorterst string of numbers. Same with 2/3.

Since 1/7 wasn't part of the original question, that leaves 3 choices to calculate. Then, since 2/11 is 0.181818, 41/99 is 0.414141 and 23/37 is 0.621621621, the answer is E, or 23/37.

With your added choice of F, F becomes the answer. But this wasn't part of the original question if I remember correctly, so no need to go there.

Alternately, you could note that dividing a number by 99 is the same as dividing it by 11x9. So you could simply get the decimal of 1/11 (0.090909) and then note that multiplying it by 2 would give you a repeating decimal of 2 digits, while dividing it by 9 and then multiplying it by an integer also yields a repeating decimal of 2 digits. Then you only need to calculate E to see that it has more than 2 digits in the decimal.
Manager
Joined: 06 Aug 2005
Posts: 194

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21 Sep 2005, 06:47
1
Also 37 = 111/3
So that will repeat fairly quickly.
In general things like 3,9,11 do.
It is the bigger primes like 7 and 13 that give longer series.
There is some interest maths underneath all this.
But to be honest working it out in each case is the safest.
You might get one question like this, or you might not get any.
Senior Manager
Joined: 04 May 2005
Posts: 265
Location: CA, USA

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21 Sep 2005, 22:16
thanks,
it seems that if m is a prime number, then n/m will have the same number of repeating digits as 1/m. That way the calcuation can be cut down a little bit
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Re: If each of the following fractions were written as a  [#permalink]

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15 Nov 2017, 21:52
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Re: If each of the following fractions were written as a &nbs [#permalink] 15 Nov 2017, 21:52
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# If each of the following fractions were written as a

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