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 more accurate information is precisely (no pun intended) what they DON’T have.
How accurate, really, were your initial numbers? And can you actually trust those last digits of your result – or are they basically just random digits, in roughly the right numerical area, giving you a false feeling of accuracy?
Errors compound. Put simply – **small errors get bigger when you mix them together**. If your numbers were, say, actually 1.23 ± 0.004 and 4.84 ± 0.004 (in other words, merely correct to roughly 2 decimal places) – the actual product could be anywhere between 5.928936 and 5.977496. It makes no sense to think that you “know” the result to 4 decimal places; actually, you don’t even know it to 1 place. About the best you can say is that it’s a few hundredths under 6.
(Yes, if we’re just talking theoretical numbers in a theoretical context, the result is precise. But for real world stuff, the end result is no better than the accuracy of your measurements – and you’d better allow for the margins of error, or you could end up with a result that is, basically, little more than garbage.)
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