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Path: utzoo!linus!philabs!prls!amdimage!amdcad!decwrl!herbison@ultra.DEC (B.J.)
From: herbison@ultra.DEC (B.J.)
Newsgroups: net.math
Subject: Re: The perils of Nutrasweet: digits of percision (a hex on you)
Message-ID: <174@decwrl.UUCP>
Date: Tue, 27-Aug-85 11:26:16 EDT
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Posted: Tue Aug 27 11:26:16 1985
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The original question was the area of a table 3 meters by 4 meters.
>> 	Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2;
>> since the initial data only had 1 digit of accuracy, that's all the final
>> answer can have.

Steven Bird says:

>Getting even more off the point, suppose we were to compute 3*4 in base 12.
>The answer of course is 10(base 12) which has 1 significant figure as required.
>10(base 12) translates to 12 +/- 6 (base 10) which I think is more acceptable
>than the 10 +/- 5 implied by 1 * 10^1 metres^2 above.

And if the calculation is done in hexadecimal, the answer is 3*4=C.
This translates to decimal as 12 +/- 0.5.

In binary the problem is 11*100=1100.  There are two significant digits
(bits) from the `11', so the decimal version of this is 12 +/- 2.

>Error analysis should be *independent* of the base used to represent numbers.
>For this reason I think there is something fundamentally wrong with the use
>of significant figures to express accuracy.

I agree with you Steven, thanks for pointing that line of reasoning out.
						B.J.