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PRACTICE / Error propagation

How uncertain is the rectangle?

A rectangular plate has measured length 20.0 ± 0.2 cm and width 10.0 ± 0.1 cm.

What is its approximate worst-case fractional area uncertainty?

Organize the givens & assumptions
  • δL/L = 0.01
  • δW/W = 0.01

Small absolute bounds, with no constraint preventing both dimensions reaching their bounds; retain first-order terms.

  1. A0.02 (2%)0.02\ (2\%)
  2. B0.01 (1%)0.01\ (1\%)
  3. C0.0001 (0.01%)0.0001\ (0.01\%)
  4. D0.0141 (1.41%)0.0141\ (1.41\%)

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