Using the criteria for numerical calculations, we find that the correct answer is
a) Keep at least a couple of extra digits beyond those needed for determining significativaes figure
Numerical calculations that involve several steps or approximations to find the correct results, must be taken into account several criteria:
- Rounding problems, which create an accumulation of errors, to reduce this effect you can include several extra significant figures in the intermediate calculations and round only to the end using the criterion of significant figures.
- For extensive computer calculations, keep in mind that the different types of numbers have a repetition period, so if possible, double-precision numbers should be used to extend the repetition period.
- The fluctuation of very small numbers due to the byte change in the computer system.
Let's review the different claims:
a) True. Keeping some extra digits reduces the problem of accumulation of errors and apply the criterion of significant figures at the end of the calculation.
b) False. When you do this the systematic errors increase significantly
c) False. This introduces a significant time cost in the calculations and does not improve the final result, it is preferable to calculate the magnitude and at the end make an estimate of the errors
d) False. This does not improve the result, but it does not create a significant time loss either, it is preferable to switch to scientific notation at the end.
Using the criteria for numerical calculations, we find that the correct answer is
a) Keep at least a couple of extra digits beyond those needed for determining significativaes figure
learn more about numerical calculations here:
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