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.
