Physics I / Propagation of Errors
Practice question · Multiple choice

You add two measured lengths: a=50.0±0.3a = 50.0 \pm 0.3 cm and b=50.0±0.4b = 50.0 \pm 0.4 cm. Assuming independent errors, the uncertainty of a+ba + b is…

Hints
  1. Independent errors sometimes push in opposite directions and partially cancel, plain addition ignores that.
  2. Independent uncertainties add like perpendicular vectors: a 3-4-5 triangle is hiding in the numbers.
Show the answer

A. 0.5 cm, combining in quadrature

Why

0.09+0.16=0.5\sqrt{0.09 + 0.16} = 0.5 cm. Quadrature is the mathematics of partial cancellation: uncorrelated wobbles add as areas, not lengths. Straight addition (0.7) is the pessimistic bound for perfectly correlated errors.

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