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When two measured quantities are added, their absolute uncertainties combine

  • A.in quadrature, as the root of the sum of squares
  • B.by simple addition of the two absolute uncertainties
  • C.by subtracting the smaller from the larger
  • D.not at all, the sum carrying no uncertainty

Answer: A

Correct answer: in quadrature, as the root of the sum of squares

\[ u = \sqrt{u_1^2 + u_2^2} \] for independent uncertainties. Simple addition would assume both errors take their maximum value in the same direction at once, which is improbable, and would overstate the combined uncertainty. Quadrature is the correct treatment when the two are genuinely independent.

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