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In lecture and in the course reader, c (speed of light) was written as 3.00 * 10^8 but my RA didn't round and said we should use 2.99 * 10^8...I know in the end it probably won't make much of a difference but on quizzes/etc., what should we be using?
I think this is more of a personal choice. Many periodic tables have different molar masses but regardless of what number you choose, if your calculations are accurate the end result is similar with a margin of error. I'd personally use 3.00*10^8 because it would make calculations easier, but there should be no problem with using 2.99*10^8 either.
I believe in lecture it was said that the value for the speed of light will be given in the problem whenever it is on quizzes/tests, so I wouldn't worry about memorizing one or the other. Still, I agree that on homework, etc. rounding up to 3.00*10^8 is probably fine.
You should always use the constant value that is given to you on the formula/constants sheet during a quiz or exam (you don't need to memorize these, as they will be given to you, so you can refer to the sheet). This way, the answer can be expected to be consistent across all students without the minor differences that come from using slightly different rounded versions of the constant.
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