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Regarding Calculator and low precision values
Authored by: Baggins on Dec 12, '05 08:57:44AM

Sorry to correct you, but you are wrong.

By definition, the LAST digit in the significant figure is the uncertain figure.

So, 13,000 in significant figures simply means that we know the 1 for certain, and know that the 3 is approximate. In other words, the value could be anywhere from 12,000 to 14,000, so you can see that no bias is introduced in rounding.

Regarding Calculator and low precision values
Authored by: jsuen on Dec 12, '05 09:56:53AM

No, thats wrong. If 2 figures are significant, those two figures are exact.

Check out rule 1:
http://dbhs.wvusd.k12.ca.us/webdocs/SigFigs/SigFigRules.html

The site also describes round-to-even.

Regarding Calculator and low precision values
Authored by: Baggins on Dec 12, '05 10:56:55AM

I'm sorry, but the site you linked is incomplete.

Significant figures are used in Physics and Chemistry to specify the accuracy of a measurement. The last digit that is significant is always an approximation or the digit at which error creeps into the measurement.

In strict notation, the significant digits are always followed by an uncertainty value.

For example, 1.234 +/-.002 has four significant figures with an uncertainty of 2 in the last digit. This means the value COULD be anywhere from 1.232 to 1.236. If no error value is listed, then it is assumed the entire digit could be incorrect, meaning the value in our example could be anywhere from 1.230 to 1.239.

A classic example of this at work is when you measure something with a ruler. Assume the ruler is marked to a tenth of an inch. Your significant digits for any measure would be to the hundredth, with the hundredth being an approximation (as judged by your eyeball).

If you were being very precise, you would then add a margin of error and a confidence level to that error. The error simply states you could be off by that amount, and the confidence level is simply the probability that you are right in saying you could be off by your error margin.

When you are performing math where significant digits are involved, the rounding rules are: 0-4 round down, 5-9 round up.

If you still doubt me, go grab a frehsman college text on Chemistry.