Hey, when we solve for significant figures, why do we completely get rid of the remaining decimals even though hey have more accurate information?
Ex. 1.23*4.84=5.9532 but we would make it 5.95 based on Sig figs, even though those last two decimals are closer to the answer. Why is this? I know it’s less accurate, though it seems like we’re losing valuable accuracy (even if it’s not perfect, it should be closer)
In: Mathematics
because the values you input in reallife-experiments/observations arent the fixed values you’re thinking off.
when an experiment got 1.23 as its result it isn’t EXACTLY 1.23 (as in 1.23000…..000), but it is possibly 1.2298 +/-0.0015, so so rounding it up to 1.23 and saying it is that value is the right thing to do because even if you go 2-3 standard deviations away, you still land at something that rounds back to 1.23
but when you put in those 1.2298 +/-0.0015 into your equation properly you will get to something like 5.9532 +/- 0.0060 (error margins just randomly chosen/estimated, didnt bother calculation, those are just for visualization purposes here)
so when you then present your result as 5.9532 when it could easily also be 5.9549 or 5.9511 would be miss-representing the accuracy of your experiment.
and even outside of experiments, when we deal with abstracted math models, it generally makes little sense to bother with additional digits if you only care about the one before the decimal point for example.
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