Re: Significance, was Re: TI-92, HELP! Significative numbe
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Re: Significance, was Re: TI-92, HELP! Significative numbers!!! Thx Ray!
My, you put a lot of thought into that. However, when scientists really do
this sort of thing, they don't have time for all of that. We just follow
some simple rules. Significant figures are all the numbers that are
important, depending on how accurate your measuring device is. For instance,
say you have two scales, one goes to one decimal place, and the other goes to
three. You weigh something, and get 1.2 and 1.200. On the first scale, you
dont know what in really comes after the 2, hense only two digits are
significant. On the second, you know for sure that there are two zeros there,
so there are four significant digits. Then you have 0.001, in which only the
1 is significant, the zeros are all placeholders. You can see already why
it would be hard to get a program to do this.
Then, when doing calculations, we don't bother with all that algebra or
+/-dx stuff, we just do this: When adding or subtracting, the answer has as
many decimal places as the original measurement with the fewest number of
decimal places. When multiplying or dividing, the answer has as many
significant figures as the original measurement with the fewest number of
sig figs. Everything else just gets rounded off. The purpose of it all
is to only keep the numbers that we are absolutely certain of. Anything that
would be affected by the +/-dx varience you spoke of is rounded off because
we are aware of the fact that we don't know that part of it.
So, deep down I suppose it's all that you said, but the application is a bit
simpler. Note that I have no problem with what you said, this is not a
flame, I just thought you and others should know what we are really talking
about here before we get too far off track. Apologies if you knew all of this
already.