A set of measurements of the ultimate tensile strength (UTS) of a new aluminium alloy gives an average of 574.16 MPa with an associated uncertainty of ± 11.56 MPa. How should you report this finding?

Question

BlackTom AI · Accepted Answer

Uncertainty-rounding rules: uncertainties should be quoted to a sensible number of significant figures (commonly one significant figure, or two if the leading digit is 1), and the reported central value should be presented to the same decimal place as the uncertainty.

1) Relevant knowledge points and concepts
- Report uncertainties with an appropriate number of significant figures (1 s.f. is standard; use 2 s.f. when the leading digit is 1 to avoid large relative rounding error).
- The reported mean should be expressed to the same decimal place as the uncertainty so the digits imply the same precision.

2) Step-by-step reasoning
- Given mean = 574.16 MPa and uncertainty = ±11.56 MPa.
- Decide how many significant figures to keep in the uncertainty. Because the leading digit of 11.56 is 1, it is common to keep two significant figures for the uncertainty (to avoid excessive rounding error). So round 11.56 to 12 MPa.

3) Calculations / intermediate steps
- 11.56 → round to two significant figures:
  - First two digits are "11"; the next digit (5) rounds the second digit up: 11.56 → 12 (MPa).
- Uncertainty becomes ±12 MPa.

4) Why the correct answer is correct
- The rounded uncertainty ±12 MPa follows the convention of using two significant figures when the first digit is 1. Option d explicitly gives that rounded uncertainty: UTS = 574.16 ± 12 MPa, matching the convention applied to the given numeric uncertainty.

5) Why the other options are incorrect
- a (570 ± 10 MPa): changes the mean and reduces the uncertainty more aggressively than justified by the data.
- b (574 ± 11.6 MPa): uses an odd mixture (mean rounded but uncertainty left with three significant figures); 11.6 is less conventional than 12 here.
- c (574.16 ± 11.56 MPa): gives too many significant figures for the uncertainty (unrounded raw uncertainty is usually not quoted to that precision).
- e, f, g, h: either drop precision incorrectly or mismatch mean/uncertainty rounding rules.

6) Conclusion / final confirmation
- Applying standard uncertainty-rounding conventions (two significant figures for an uncertainty beginning with 1) gives ±12 MPa, so the reported result in the list that matches this is UTS = 574.16 ± 12 MPa (option d), which agrees with the provided correct answer.

A set of measurements of the ultimate tensile strength (UTS) of a new aluminium alloy gives an average of 574.16 MPa with an associated uncertainty of ± 11.56 MPa. How should you report this finding?单项选择题

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