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Precision and significant figures

In this course, you are expected to perform calculations to a relative accuracy of 1%: i.e., to three significant figures. Since rounding errors tend to accumulate during lengthy calculations, the easiest way in which to achieve this accuracy is to perform all intermediate calculations to four significant figures, and then to round the final result down to three significant figures. If one of the quantities in your calculation turns out to the the small difference between two much larger numbers, then you may need to keep more than four significant figures. Incidentally, you are strongly urged to use scientific notation in all of your calculations: the use of non-scientific notation is generally a major source of error in this course. If your calculators are capable of operating in a mode in which all numbers (not just very small or very large numbers) are displayed in scientific form then you are advised to perform your calculations in this mode.

Richard Fitzpatrick 2006-02-02