Part A: Propagation using your Station 1 measurements

Part A: Propagation using your Station 1 measurements

You measured the dimensions of an object with both a ruler and digital calipers. Now you will calculate the volume of that object using each instrument’s measurements and compare the results.

Why this matters: Your volume formula may include the mathematical constant π. Since π is not a measured quantity it carries no uncertainty — treat it as exact in your propagation calculation.

1. Write down the formula for the volume of your object. Identify which quantities in the formula are measured and which are exact.
2. Using your caliper measurements, calculate the volume of the object. Show all steps.
3. Propagate the uncertainty through your calculation using Rule 1 and Rule 2 as needed. Show all steps.
4. Report your result in correct form and justify your rounding.
5. Now repeat steps 2–4 using your ruler measurements instead.
6. Compare your two results:
   • Do they agree within their uncertainties?
   • How does the uncertainty in the final result differ between the two instruments?
   • What does this tell you about the cost of using a less precise instrument?