Two students are discussing how uncertainty behaves when two measured quantities are added

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

Two students are discussing how uncertainty behaves when two measured quantities are added. Consider the following information: A balance gives a mass of

125.6\,\text{g}

with an estimated uncertainty of

\pm0.2\,\text{g}

and another mass of

78.34\,\text{g}

with an estimated uncertainty of

\pm0.05\,\text{g}

. (i) Define absolute uncertainty and relative uncertainty in the context of a single measurement. (ii) Without carrying out any numerical addition, identify which of the two measurements will contribute more to the uncertainty in their combined mass. Justify your answer in not more than three sentences. (iii) When the two masses are added, to which decimal place should the final result be reported? Explain the reason for choosing that particular place value.

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