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20 replies to this topic

#1 Ploper

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Posted 08 December 2007 - 05:18 PM

you can easily divide a cake between 3 people.
just cut it into thirds.
but you cannot divide a cake between 3 people
by cutting pieces that are 33% percent of the whole
because someone will wind up getting 34%
and you can't do 33.3333333%
cuz someone will still get more than the others
so if you can divide it into thirds, then why can't you divide into three pieces with percents?
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#2 Martini

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Posted 08 December 2007 - 11:06 PM

but you cannot divide a cake between 3 people


You're aware that you're giving false information in your riddle, right?

by cutting pieces that are 33% percent of the whole
because someone will wind up getting 34%
and you can't do 33.3333333%
cuz someone will still get more than the others


Spoiler for solution


so if you can divide it into thirds, then why can't you divide into three pieces with percents?


You can.
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#3 spoxjox

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Posted 09 December 2007 - 02:23 AM

so if you can divide it into thirds, then why can't you divide into three pieces with percents?


Because we use base 10 numbering. (Of course, all numbering systems would be called base 10 in their own base...but you know what I mean.) If we used base 3 numbering, then 100 would represent the decimal number 9, and a third would be represented by the number 10%. (Note that one-half, or what in decimal we call 50%, would not be representable by a terminating "decimal" expansion in base 3 percent representation. It would be 11.1111111111...%)
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#4 timforyou12

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Posted 09 December 2007 - 09:50 PM

In other words, you could cut it using percents, however, you wouldn't due to the fact that fractions are more precise than percents.
33.33333333333333333333333333333333333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333333333333333333.....% would still technically be 1/3 it just never ends, so you can't see the fact that it is 1/3.
If you were to go to the end of the infinite decimal, you would find that it is.

however, this is all beside the point, because if I had a cake I would simply eat it all and not share!!!!
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#5 Martini

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Posted 09 December 2007 - 10:12 PM

fractions are more precise than percents.


No, they're not.

1/4 = .25
1/3 = .333...

Remember, the = sign is never used loosely in mathematics. 1/3 is exactly equal to .333...

And yes, .999... is equal to 1.
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#6 bonanova

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Posted 10 December 2007 - 04:58 AM

fractions are more precise than percents.


Well, all rational numbers do have exact representations as integer ratios; but not as finite-length decimals.
But irrational numbers [pi, e.g.] lack exact representations both ways.
pi ~= 22/7
pi ~= 3.1415926536 ...
Now, although the precision of both representations can be improved to an arbitrary level,
it's much easier to add a digit to the decimal representation than it is to find the next-more-precise integer ratio.

Also, just as 1/3 may look more compact than 0.333333 ...
one can say .3 looks more compact than 1/0.33333 ...
But to be fair .3 and 3/10 are about the same.

Your comment is interesting but not generally true.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#7 Ploper

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Posted 12 December 2007 - 01:54 AM

thank you I guess
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#8 Martini

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Posted 12 December 2007 - 08:06 AM

Ya know what I love about you, Ploper? It always seems you genuinely appreciate being shown that something has a different answer than what you expected without letting your ego get in the way. I think most of us would be better off if we could do that. Now if we could only convince you that if a parent has two kids and at least one of them is a girl, the probability that the other kid is also a girl is 1/3. ;)
Anyway, glad you're here and I hope you'll be sticking around for a long time to come.
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#9 carlosn27

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Posted 12 December 2007 - 05:34 PM

speaking of numbers, did you know that the average person has less than one leg?
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#10 Ploper

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Posted 13 December 2007 - 01:31 AM

thanks Martini
but that doesn't stop me from being stubborn.

I don't understand how .999 could = 1
becuase if you look at what isn't there, the .001
that .001 is something
if .999=1 then .001 must equal 0
but something, no matter how small, is more than nothing.
unless they all have 33.333333% and throw away 0.000001% (which, granted, is next to nothing)
the equal value cannot be expressed as a decimal.

I know someone will correct me and we'll all be on our way.
I learn from saying stupid things then havin people on here correct me
it's the reason why people I know think I'm smart
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