Simple Uncertainty/Sig Fig Question

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SUMMARY

The discussion focuses on the proper method for calculating uncertainty when subtracting two measurements: 50.00 mL ± 0.05 mL and 14.3 mL ± 0.1 mL. The correct result is 35.7 mL ± 0.15 mL, derived by using the root sum square method for uncertainties. It emphasizes that the number of decimal places in the final answer cannot exceed that of the least precise measurement, which in this case is the second value with one decimal place.

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Homework Statement


This is for a lab. I have two values that I need to subtract, so I am pretty sure I am supposed to add up uncertainty. I have also been told that the uncertainty decimal places should match up with the decimal places on the value itself.

50.00mL ± 0.05mL – 14.3mL ± 0.1mL =

Homework Equations

The Attempt at a Solution


35.7mL ± 0.15mL?
 
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Matching up the decimal places between error and value is generally right, why do you know one pair of values to two decimal places and the other pair to only one? It seems odd.
Assuming there is a good reason for that, there are two more points to consider. Generally,one argues that you would be unlucky for the errors to reinforce to the maximum extent, so instead take a statistical approach. Specifically, take the root sum square of the errors. Next, you cannot quote more decimal places in the answer than your worst case input value.
 

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