Os envío una página del libro “Data Reduction and Error Analysis for the Physical Sciences”, Philip R. Bevington y D. Keith Robinson (Mc Graw Hill, Thirg Edition, 2003). Me la ha hecho llegar un catedrático mayorcito ante mis preguntas sobre las cifras significativas.
No especifica mucho, pero se puede tomar como "lo único que está estipulado claramente". Por ejemplo, la 239 del general 35, que da como respuesta 0.0625, está claramente mal. Pero se puede tragar 0.12, o 0.26: una segunda cifra si la primera es pequeña...
Va:
Significant Figures and Roundoff
The precision of an experimental result is implied by the number of digits recorded in the result, although generally the uncertainty should be quoted specifically as well. The number of significant figures in a result is defined as follows:
1. The leftmost nonzero digit is the most significant digit.
2. If there is no decimal point, the rightmost nonzero digit is the least significant digit.
3. If there is a decimal point, the rightmost digit is the least significant digit, even if it is a 0.
4. All digits between the least and most significant digits are counted as significant digits.
For example, the following numbers each have four significant digits: 1234, 123,400, 123.4, 1001, 1000., 10.10, 0.0001010, 100.0. If there is no decimal point, there are ambiguities when the rightmost digit is 0. Thus, the number 1010 is considered to have only three significant digits even though the last digit might be physically significant. To avoid ambiguity, it is better to supply decimal points or to write such numbers in scientific notation, that is, as an argument in decimal notation multiplied by the appropriate power of 10. Thus, our example of 1010 would be written as 1010. or 1.010 X 103 if all four digits are significant.
When quoting an experimental result, the number of significant figures should be approximately one more than that dictated by the experimental precision. The reason for including the extra digit is to avoid errors that might be caused by rounding errors in later calculations. If the result of the measurement of Example 1.1 is L = 1.979 m with an uncertainty of 0.012 m, this result could be quoted as L = (1.979 ± 0.012) m. However, if the first digit of the uncertainty is large, such as 0.082 m, then we should probably quote L = (1.98 ± 0.08) m. In other words, we let the uncertainty define the precision to which we quote our result.
When insignificant digits are dropped from a number, the last digit retained should be rounded off for the best accuracy. To round off a number to fewer significant digits than were specified originally, we truncate the number as desired and treat the excess digits as a decimal fraction. Then:
1. If the fraction is greater than Yi, increment the new least significant digit.
2. If the fraction is less than Yi, do not increment.
3. If the fraction equals Yi, increment the least significant digit only if it is odd.
The reason for rule 3 is that a fractional value of Yi may result from a previous rounding up of a fraction that was slightly less than Yi or a rounding down of a fraction that was slightly greater than Yi. For example, 1.249 and 1.251 both round to three significant figures as 1.25. If we were to round again to two significant figures, both would yield the same value, either 1.2 or 1.3, depending on our convention. Choosing to round up if the resulting last digit is odd and to round down if the resulting last digit is even, reduces systematic errors that would otherwise be introduced into the average of a group of such numbers. Note that it is generally advisable to retain all available digits in intermediate calculations and round only the final results.
