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
The Sun is a long way away, the average distance from Earth is more or less defined by one astronomical unit, which is ninety-two million nine hundred and fifty-five thousand eight hundred and seven miles.
That’s a long way, imagine if we could drive a car at 100mph. How long would it take us to travel ninety-two million nine hundred and fifty-five thousand eight hundred and seven miles? The distance between the Earth and the Sun varies and sometimes it’s more than ninety-two million nine hundred and fifty-five thousand eight hundred and seven miles.
Notice how the above obscures the key information. To focus on what is *significant*, we use significant figures. If I talk about the distance to the Sun being 93 million miles, sure I’ve thrown away some accuracy, but it allows us to focus on the concept, making it easier for us to absorb and make comparisons.
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.
For some other reason (usually measurement accuracy) we know our data isn’t that accurate, so we remove significant figures as a convenient way to communicate the lack of accuracy
Firstly, I would like to point out that it isn’t more accurate, it’s more precise, to use more significant figures. And the reason to not use so many depends on the application. In the real world, there is rarely a need to go to lots of significant figures, and also a lot of things can’t measure to such precision anyway.
If it’s pure math, you can keep those digits.
If it’s anything applied, like a measurement, then you can’t keep those digits because you don’t actually know that precision. Your measurement tool is accurate to X.xx; how can it possibly verify that the math is correct to X.xxxx? This is to prevent mathematics from creating an impossible situation, where a mathematically derived precision is unreachable by physical means.
In some fields of engineering, you can’t go ahead if you measure something is 3.79 but the specification requires 3.790. You need to meet/match specification, and specifications can only be as accurate as the measurement tools used to derive them.
5.95 is a shorthand for 5.9532 +- 0.00XX
It’s just to save space, and to prevent someone from thinking the 32 has any real meaning.
Yes it’s a better guess than 5.9500 but we already assume 5.95 means 5.95XX and not followed by zeros.
Well sig figs has everything to do with accuracy. Scientist want to convey the accuracy of calculated numbers. Thus, your answer can only be as accurate as your least accurate measurement. We cut those extra numbers off not to be more accurate but to remain equally accurate as before.
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