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Terminating decimals

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Master | Next Rank: 500 Posts
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by tanyajoseph » Mon Sep 03, 2007 11:15 am
hich of the following has a decimal equivalent that is a terminating decimal?

10/189
15/196
16/225
25/144
39/128

Is there any quick way to solve these problems than having to meticulously work through each fraction and thus eat up valuable time?
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by givemeanid » Mon Sep 03, 2007 12:53 pm
Denominators with only 2 and 5 as factors will always terminate no matter what the numerator is.

Denominators will 3, 7... will not terminate unless numerator is completely divisible.

Looking at the denominators, 128 = 2^7. So, E will terminate no matter what.
Check other choices. They will have 3 or 7 (or 11) as a factor.
So It Goes
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by mateodude » Sun Oct 07, 2007 10:13 am
Yes, very useful. Thanks.

How about determining, among a selection of fractions, which would have the longest sequence of differenent decimal digits? Is there a shortcut or trick?

Simple example would be:

2/11
1/3
41/99
2/3
23/37

I understand that one could immediatly rule out a couple of these.
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