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The periodic table given on the test was the one on his website, so I would use that one. I would also go to the last decimal place given on the periodic table and not round your final answer till the end.
If we use the rounded version of the atomic mass (let's say to the hundredths) and correctly use significant figures, would our answer be wrong if the answer we get is right according to the rounded calculations we made?
You should base your sig figs off of what the problem gives you I think. If 250 ml is your smallest given, your final answer should have 2 sig figs. I don't think constants like 273.15 K contribute to sig figs, but you might want to check that.
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