Exam-style question
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A student measures the length of a metal rod as 50.0 cm with a precision of ±0.5 cm. If the student measures the width as 10.0 cm with a precision of ±0.2 cm, calculate the combined uncertainty in the area of the rod.
Model answer
What a good answer should say
- The combined uncertainty in the area is ?15 cm?.
Explanation
Why this works
For multiplication, add the fractional uncertainties. The area is 50.0 cm ?
10.0 cm = 500 cm?. The fractional uncertainties are 0.5/50.0 = 0.01 and 0.2/10.0 = 0.02, so the combined fractional uncertainty is 0.03.
Therefore 0.03 ? 500 cm?
= 15 cm?.
Common mistake
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