| Excerpt |
|---|
The non-zero individual digits ( figures ) in a number that are of importance and essential to convey the value and the precision needed or measured. |
In the number 55.5 , for example, there are three significant digits, and all three should be reported if we want to accurately convey the information and the precision of that number. if we were to report this number as 55 we would be leaving out part of the information, and not being as precise as the original number. On the other hand, the average of the numbers 55.5, 60.8, and 42.7 is 33.0 The last "zero" is important to convey the three-significant-digit precision. If we were to take the average of those three numbers and 30.7, the correct answer would be 32.4, not the "exact" value of 32.425, since that implies a greater precision of five figures, and our result cannot have more significant digits than our input values.
Treating the error or uncertainty using the rule "always use the same number of significant figures in your answer as in your original quantities" can lead to under-or over reporting the actual error by an order of magnitude and is too gross an approximation to use for real data or anything else of importance. In the above example, if 55.5 and 60.8 (each presumably with an error around 0.1) were added to give 116.3 (presumably also with an error around 0.1), the result would be reported as 116 (keeping just three significant figures), implying an error of about 1. On the other hand if they were subtracted, the difference would be reported as -5.30, implying an error of only 0.01 when the actual error is is somewhat increased by combining them and is at least 0.1.