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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.

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