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Topic: How many digits? (Read 307 times) |
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BNC
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How many digits?
« on: Jun 3rd, 2004, 5:37am » |
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If I were to write the number 22004 followed by the number 52004 (both in explicit decimal notation), how many digits would I write?
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Grimbal
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Re: How many digits?
« Reply #1 on: Jun 3rd, 2004, 6:22am » |
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Ten. But some of them more than once. 
More seriously, I would propose: ceil(log10(2)*2004)+ceil(log10(5)*2004) which I leave to the reader to calculate.
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harpanet
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Re: How many digits?
« Reply #2 on: Jun 3rd, 2004, 6:42am » |
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I'll do the calculation by hand and let you know next year.
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BNC
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Re: How many digits?
« Reply #3 on: Jun 3rd, 2004, 7:08am » |
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on Jun 3rd, 2004, 6:22am, Grimbal wrote:| ... I would propose: <hidden> |
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explaining how you arrived at an answer is more valuable than the answer itself !
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Grimbal
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Re: How many digits?
« Reply #4 on: Jun 3rd, 2004, 7:53am » |
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on Jun 3rd, 2004, 7:08am, BNC wrote:| explaining how you arrived at an answer is more valuable than the answer itself ! |
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I didn't give the answer, I just told how I computed it!
OK. A N-number digit can have values 10^(N-1)<=value<10^N.
so, (N-1)<=log10(value)<N which means that if you know the value and want to know the number of digits, you have N=floor(log10(value))+1. (I used ceil because in this case, the logs are not integers)
If for example value = 3^123, log10(value) = 123*log10(3).
This is valid for all 3 in {2,5} and any 123 in {2004}.
But I realised there is a much simpler way to get to the same result.
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towr
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Re: How many digits?
« Reply #5 on: Jun 3rd, 2004, 8:30am » |
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::log10(2) + log10(5) = 1, so I get 2005
Because ceil(a+b) <= ceil(a) + ceil(b) <= ceil(a+b) + 1, and in this case a+b is an integer and a and b aren't.::
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| « Last Edit: Jun 3rd, 2004, 8:32am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Grimbal
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Re: How many digits?
« Reply #6 on: Jun 3rd, 2004, 8:39am » |
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Exactly. Since 2*5=10.
::You have 2 numbers of which the product is 10^2024. It must have 2005 digits, since they are not of the form 10^n.::
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