Re: Numbers from 1-10

On Fri, 29 Aug 2003 23:30:23 -0400, Dennis Paul Himes <himes@...>
wrote:

>Andrew Patterson <endipatterson@...> wrote:
>>
>> You will notice that ten can be divided by one two and five,(three
>> factors) but twelve can be divided exactly by one, two, three, four and
>> six (five factors)and indeed although five and seven don't divide twelve
>> exactly, they do divide to produce a non recurring fraction in base
>> twelve. Note that to write 1/3 or 2/3 as a decimal you get a recurring
>> fraction.
>
>    What do you mean by "non recurring"?  Do you mean "terminating"?
>  If so, you're wrong.
  1/5 is .249724972497... in base 12 and 1/7 is .183518351835...
> in base 12.  In general, if the denominator of a fraction (expressed in
lowest
>terms) is divisible by any prime which is not a divisor of the base, then
>the equivalent decimal expansion will not terminate.
>
>                 Dennis Paul Himes    <>    himes@cshore.com
>                   http://home.cshore.com/himes/dennis.htm
>        Gladilatian page: http://home.cshore.com/himes/glad/lang.htm
>
Yes, that is what I meant but whoops, I got it wrong. Nevertheless, twelve
still does have proportionately more factors than ten, even if 5/12 and
7/12 are surds.

Andrew Patterson.