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Propagation of Uncertainty: Multiplication and Division

This guide explains how to calculate volume uncertainty in chemistry experiments involving measurements. Using the provided dimensions, we measure a rectangular prism with length 25.21 ± 0.03 cm, width 21.24 ± 0.03 cm, and height 15.20 ± 0.02 cm. We find the volume to be 8138.99808 cm³, and through the propagation of uncertainty methods, we determine the final volume and its uncertainty as 8140 ± 20 cm³. This emphasizes the importance of uncertainty in scientific measurements.

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Propagation of Uncertainty: Multiplication and Division

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  1. Propagation of Uncertainty: Multiplication and Division CHEM 210

  2. Measure a Volume • Length: 25.21 ± .03 cm • Width: 21.24 ± .03 cm • Height: 15.20 ± .02 cm • Volume is 8138.99808 cm3. • What is the uncertainty in volume?

  3. Measure a Volume

  4. Measure a Volume Get the result first

  5. Measure a Volume Abs. unc. Rel. unc. = Value

  6. Measure a Volume Square the relative uncertainty

  7. Measure a Volume Add the (rel. unc.)2

  8. Measure a Volume Take the square root

  9. Measure a Volume Abs. unc. solve for Rel. unc. = Value

  10. Measure a Volume The volume is 8140 ± 20 cm3

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