Calculating Weighing Uncertainty

Raj had a question for Paul concerning significant figures. When his group measured the weight in a four decimal place balance, i.e., 0.0001 grams, he wondered how they should go about rounding the value.

	RE: Calculating Weighing Uncertainty Dear Raj,      First, determine the linearity for the balance from the calibration certificate. For this example, we will assume ± 0.15 mg for a 4-place balance. Balance manufacturers recommend the use of a rectangular distribution to convert the linearity contribution to a standard uncertainty. Therefore, the balance linearity contribution is 0.15mg/(3)1/2 = 0.09 mg. This contribution may have to be counted twice if the sample is weighed by difference -- once for the tare and once for the gross weight, giving a standard uncertainty that equals (2 x (0.09)2)1/2 = 0.13 mg.      Thusly, a weight of 0.0413 g would have a standard uncertainty of 0.13 mg. Using a coverage factor of 2, an uncertainty of 0.26 mg (that would be rounded to 0.3 mg) would be reported. Using this example, the weight would be reported as 0.0413 grams ± 0.0003 grams and the number of significant figures is 3. I hope this helps. Please see this our corresponding article, Significant Figures and Uncertainty, for additional help with significant figures and uncertainty calculations.     Paul R. Gaines, Ph.D. Serving you in chemistry