[ale] [OT] Help with Significant Figures Explaination

[Sean McNealy]

Unfortunately, significant figures are very representationally dependent.

Doing measurements and math in base10 is different than base2.  You
will be looking at different numbers the entire time.  They are
however "close enough", since they're within some proportionally small
delta that has been considered "insignificant".

Let's say I measure something (with a precision to about 0.1) and I
get 2.7 somethings.
My computer's A/D converter, assuming its measurement equipment is
about as precise, 10.110 somethings.  (This is 2.75 in decimal, but
only if we remove the meaning we've placed on significant figures.)

Anyway, significant figures are just a simplified way to represent and
model a statistical error (like a standard deviation) without doing a
lot of work.  Have enough digits and you're within practical
tolerances anyway.

On Fri, Oct 17, 2008 at 4:50 PM, tom <tfreeman at intel.digichem.net> wrote:
> I have seen something resembling a justification _once_ before this
> recent search. On this last search I found some hand waving from
> statistics, but given the level of numeric sophistication, I
> should consider something a little less sophisticated.
>
> On Fri, 17 Oct 2008, Ed Cashin wrote:
>
>> On Fri, Oct 17, 2008 at 12:58 PM, Jim Kinney <jim.kinney at gmail.com> wrote:
>> ...
>>> The definition I was taught and still use is the least significant digit
>>> is 1/2 the smallest MARKED unit on the measuring device. So a meter
>>> stick marked to the millimeter is good to .5mm. By eye, a reasonable
>>> person can decide if something is closer to 1mm or 2mm but judging
>>> beyond that is too imprecise.
>>
>> I think that's the working definition I learned in high school.
>> It seems reasonable, practical, and easy to justify.
>>
>> Do you know of any authoritative source that popularized
>> this way of thinking about significant digits?  I don't know
>> whether my teachers cited an authority.  I think they just
>> presented it as self evident.
>>
>>
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