Exam-style question
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A measurement of a liquid's volume is recorded as 250.0 mL with an uncertainty of ±5.0 mL. If this volume is used to calculate the density of the liquid, how do you combine the uncertainties when calculating density if the mass is measured as 500.0 g with an uncertainty of ±2.0 g?.
Model answer
What a good answer should say
- The combined uncertainty in density is about ?0.05 g/mL.
Explanation
Why this works
For density, divide mass by volume, then add the fractional uncertainties because density uses division. The density is 500.0 g / 250.0 mL = 2.0 g/mL.
The fractional uncertainties are 2.0/500.0 = 0.004 and 5.0/250.0 = 0.020, giving 0.024. Multiplying by 2.0 g/mL gives 0.048 g/mL, so the combined uncertainty is about ?0.05 g/mL.
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