Question

For a recent laboratory session we were asked to weight a 20mL beaker three times on an analytical scale. Each time, we were asked to determine the weight to within +/- 0.1mg. I am just a little confused about what this means as I have never been asked to round this way. The three values are: 13.5448g, 13.5436g, and 13.5435g. What would these three measurements actually be when applying this uncertainty?

EDIT: Please let it be known that I understand the math and that is not what I am referring to. I was specifically wondering about the semantics since I know balances have uncertainty but was unsure what this specific wording meant.

EDIT2: I have corrected first value

Answer 1

The three measurements of 13.5448g, 13.5436g, and 13.5435g on an analytical scale with an uncertainty of ± 0.1mg should be reported as 13.5448g ± 0.0001g, 13.5436g ± 0.0001g, and 13.5435g ± 0.0001g.

Step-by-step explanation:

When you're asked to determine the weight of a 20mL beaker to within ± 0.1mg on an analytical scale, you're dealing with the concept of measurement uncertainty.

This means that although the scale can measure weight very precisely, there's a small margin of error inherent to any measurement.

Your three measurements of 13.5448g, 13.5436g, and 13.5435g each have an uncertainty of ± 0.1mg, or ± 0.0001g. Thus, these values would be reported with this uncertainty factored in, which indicates the range within which the true value lies.

The corrected values would be 13.5448g ± 0.0001g, 13.5436g ± 0.0001g, and 13.5435g ± 0.0001g, respectively.