1.11:
Significant Figures in Calculations
Significant figures help achieve certainty in mathematical operations, too. In addition or subtraction, the result should be rounded off to have the same number of decimal places as the measurement with the fewest decimal places.
Rounding down should be performed when the last digit is below 5, and rounding up carried out when it is 5 or above. Other rounding methods are sometimes used when the last digit is 5.
For instance, the sum of 2.052 and 1.2 is rounded off as 3.3.
However, while multiplying or dividing, the result should be rounded to have the same number of significant figures as the measurement with the fewest significant figures. Thus, the product of 2.052 and 1.2 is rounded off as 2.5.
1.11:
Significant Figures in Calculations
Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:
- When adding or subtracting numbers, round the result to the same number of decimal places as the number with the least number of decimal places.
- When multiplying or dividing numbers, round the result to the same number of digits as the number with the least number of significant figures.
- If the digit to be dropped (the one immediately to the right of the digit to be retained) is less than 5, "round down" and leave the retained digit unchanged.
- If the digit to be dropped (the one immediately to the right of the digit to be retained) is 5 or greater, "round up" and increase the retained digit by 1. Alternative rounding methods may also be used if the dropped digit is 5. The retained digit is rounded up or down, whichever yields an even value.
An important note is that rounding of significant figures should preferably be done at the end of a multistep calculation to avoid the accumulation of errors at each step due to rounding. Thus, significant figures and rounding facilitate the correct representation of the certainty of the measured values reported.
This text is adapted from Openstax, Chemistry 2e, Section 1.5: Measurement Uncertainty, Accuracy, and Precision.