Simple Uncertainty/Sig Fig Question

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When subtracting values with uncertainties, the total uncertainty is typically calculated using the root sum square method rather than simply adding the uncertainties. The decimal places of the uncertainty should align with the precision of the measured values, which can lead to confusion when different values have varying decimal places. In this case, the subtraction of 50.00mL ± 0.05mL and 14.3mL ± 0.1mL results in 35.7mL, but the uncertainty should be calculated as 0.15mL based on the statistical approach. It's important to note that the final result should not have more decimal places than the least precise measurement. Understanding these principles ensures accurate reporting of measurements and uncertainties.
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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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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