The **rounding error** is the difference between a rounded numeric value and the actual value. For example, if the actual value is 2.9979245 x 108 and it is rounded to three decimal places, the rounded value would be 2.998 x 108. The rounding error in this case would be 0.00007542 x 108. It is important to consider how many significant digits should be included in the reported measurement. In this case, since only the leftmost 3 of 3.28 is safe, it is likely that the value will be rounded to 3.3 g. But what does this figure mean for someone else who sees it in their report? The 3.3 g value implies an uncertainty of 3.3 ± 0.05 g, meaning that the actual value is likely to be between 3.25 g and 3.35 g.

This range is 0.02 g lower than the uncertainty associated with the original measurement, so rounding has introduced a bias of this amount in the result. Although this bias is less than half of the uncertainty of ±0.05 g in weighing, it can still become significant if several values that were rounded are combined in one calculation. On the other hand, **truncation error** is the error that occurs when an infinite sum is truncated and approximated to a finite sum.

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