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If each of the following fractions were written as a [#permalink]
 05 Apr 2008, 01:55
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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? 2/11 1/3 41/99 2/3 23/37 I am marching thru the OG, this is simple, but just wonder anyone got better trick for repeating decimal (hmm obviously if we play division game for A, B, D we can find; but i try to optimize calculation time  )
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 02:25
AlbertNTN wrote: If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits? 2/11 1/3 41/99 2/3 23/37 I am marching thru the OG, this is simple, but just wonder anyone got better trick for repeating decimal (hmm obviously if we play division game for A, B, D we can find; but i try to optimize calculation time ) I remember in one post Walker had some nice explaination about the terminating and repeating fraction. He said that "1/17 has how many repeating numbers? (p-1) = 16 numbers". So I think E is my choice because E will have 37-1 =36 repeating digits? Correct me if I wrong you and Walker 
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 02:25
E1. reduce fraction if it is possible. Here we have all proper fractions. 2. because numerator does not influence on period of sequence, set all numerators to 1: 1/11, 1/3, 1/99, 1/3, 1/37 3. transform all fraction to the denominator such as 9, 99, 999 .....: 9/99, 3/9, 1/99, 3/9, 1/374. 1/37 we cannot write out as a fraction with denominator of 9 or 99. (actually we can with 999 but this is not necessary here) So, E is a winner.
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 02:28
sondenso wrote: I remember in one post Walker had some nice explaination about the terminating and repeating fraction. He said that "1/17 has how many repeating numbers? (p-1) = 16 numbers". So I think E is my choice because E will have 37-1 =36 repeating digits? Correct me if I wrong you and Walker I remember that I even proved rule with 99....999 by means of geometrical progression.... But it say that we should count 9 in 99...999 denominator. 
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 05:27
nice to see the 9 rule, is it some fundamental property of arithmetic? thanks
sodenso i don't think the rule works with 1/37 (only 3 repeated numbers) ...
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 08:03
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I found that: 7-t592137-t57168
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 15:14
kool thank u. It seems that end of this month we can't reach u huh haha. jk, enjoy ur Harvard trip
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 17:20
AlbertNTN wrote: kool thank u. It seems that end of this month we can't reach u huh haha. jk, enjoy ur Harvard trip Thanks
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Re: PS - repeating decimal [#permalink]
05 Apr 2008, 21:24
AlbertNTN wrote: nice to see the 9 rule, is it some fundamental property of arithmetic? thanks
sodenso i don't think the rule works with 1/37 (only 3 repeated numbers) ... Thank you, I got it! Forgot! Thanks Walker also and wait to hear your share about your trip to US coming!
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Re: PS - repeating decimal [#permalink]
01 May 2008, 04:47
Quote: I remember in one post Walker had some nice explaination about the terminating and repeating fraction.
He said that "1/17 has how many repeating numbers? (p-1) = 16 numbers". So I think E is my choice because E will have 37-1 =36 repeating digits?
Correct me if I wrong you and Walker
would you please point me to Walker post.
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Re: PS - repeating decimal [#permalink]
01 May 2008, 05:32
AlbertNTN wrote: If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits? 2/11 1/3 41/99 2/3 23/37 I am marching thru the OG, this is simple, but just wonder anyone got better trick for repeating decimal (hmm obviously if we play division game for A, B, D we can find; but i try to optimize calculation time ) I did this in my head in bout 2 min. its not really that bad. B,D elim right off the bat. A. just solve out, you get .1818 C again just solve out you get .4141 No need to test for E.
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Re: PS - repeating decimal
[#permalink]
01 May 2008, 05:32
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