Paper in physics - calculations; rounding or not? I'm currently a high schooler, and I'm writing my first scientific paper. The result is fairly simple, and it is nothing too special, but I see it as a nice way to prepare myself for the academic world.
The paper involves a lot of calculations and I'm actually wondering how I should approach rounding to make it as scientific as possible.
My own guess would be scientific rounding in the intermediate steps, but using the 'correct' value in further calculations. Is this correct?
 A: Preferably, you should work symbolically for as long as possible and postpone filling in any specific values until you have a final equation. Of course you don't have to overdo it either, but generally you can assess quite easily when it feels natural to write down a (significant) intermediary result.
Concerning the notation of such a result, error propagation would yield the uncertainty on the obtained value. For intermediary results, we usually round (upward) the error to 1 significant figure and then give the value to the same accuracy, accompanied by $\pm$ the rounded error.
So for example, say you find a value $4.358172\,\text{m/s}$ for some speed you calculated from several measurements. And say the uncertainty you find by application of error propagation is $0.01267\,\text{m/s}$. The rounded error for this intermediary result is $0.02\,\text{m/s}$ (remember, we always round the error upward) and therefore we denote the result as $(4.36\pm0.02)\,\text{m/s}$.
For final results, we round the error (upward) to 2 significant figures, but the rest stays the same. So if our example above were a final result, we would denote it as $(4.358\pm0.013)\,\text{m/s}$.
