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If each of the following fractions were written as a

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Manager
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If each of the following fractions were written as a [#permalink] New post 05 Apr 2008, 00:55
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A
B
C
D
E

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100% (01:13) correct 0% (00:00) wrong based on 3 sessions
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] New post 05 Apr 2008, 01:25
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 :lol:
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Re: PS - repeating decimal [#permalink] New post 05 Apr 2008, 01:25
Expert's post
E

1. 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, 1/37
4. 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] New post 05 Apr 2008, 01:28
Expert's post
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 :lol:


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. :wink:
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Re: PS - repeating decimal [#permalink] New post 05 Apr 2008, 04:27
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] New post 05 Apr 2008, 07:03
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Expert's post
I found that:

7-t59213

7-t57168
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Re: PS - repeating decimal [#permalink] New post 05 Apr 2008, 14:14
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] New post 05 Apr 2008, 16:20
Expert's post
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] New post 05 Apr 2008, 20:24
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! :lol:

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] New post 01 May 2008, 03:47
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] New post 01 May 2008, 04:32
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.
Re: PS - repeating decimal   [#permalink] 01 May 2008, 04:32
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