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Terms like percentage uncertainty, percentage error, least count, uncertainty, precision and accuracy are confusing the heck out of me.

I know that precision means closeness of the measured values, i.e if we measure the value of g and get 3 measurements, i.e 7.8, 7.6, 7.7, these will be called precise, but NOT accurate.

But when we have something like (22.5 ± 0.1) cm given with the accuracy being ±0.004, what would that mean? Does it mean that the precision is 0.1 cm, i.e all the measurements we get will vary up to 0.1 cm and that the TRUE measurement will be between 22.5004 and 22.496?

I've been taught that precision=uncertainty=least count. So, does that mean when we've been asked to find RELATIVE uncertainty/percentage uncertainty, we tend to find the ACCURACY and not the absolute uncertainty, because Accuracy = Uncertainty/measured value?

My book has messed all these terms up and I'm having a headache trying to grasp my head around what all these numbers and terms MEAN. Any help will be appreciated :)

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Well, 0.004 is the relative uncertainty corresponding to those measurement results - note that $0.1/22.4\approx 0.004$. From a terminology perspective, I would agree that this is a question of precision. I'd need a direct quote from a source using the word "accuracy" in order to speak more on how appropriate the term is to the situation.

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  • $\begingroup$ If 0.004 is the relative uncertainty and thus, precision, then, what does 0.1 represent? $\endgroup$
    – ihateelectricalphysics
    Commented Mar 19, 2021 at 20:22
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    $\begingroup$ @ihateelectricalphysics $0.1$ cm is the actual measurement uncertainty; $0.004$ is the uncertainty expressed as a fraction of the measured value. You could equivalently say that the measured length is $22.4 \text{ cm} \pm 0.1\text{ cm}$ or $22.4\text{ cm} \pm 0.4\%$. $\endgroup$
    – J. Murray
    Commented Mar 19, 2021 at 20:25
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    $\begingroup$ So.. 0.1 cm is the actual precision, but 0.004 is the precision being expressed as a fraction of the measured value? Because, I think, if that's correct, 22.4cm ± 0.1 cm can be represented as 22.4 cm ± (0.4%*22.4)cm, no? $\endgroup$
    – ihateelectricalphysics
    Commented Mar 19, 2021 at 20:57
  • $\begingroup$ @ihateelectricalphysics Yes. It's often much more convenient to work with relative uncertainty than the actual uncertainty as measured in e.g. centimeters. Which one you use depends on what you're trying to say, and to a certain degree on personal preference. $\endgroup$
    – J. Murray
    Commented Mar 19, 2021 at 21:06
  • $\begingroup$ Right. That makes sense. There's a line in my book that states: Accuracy = Least Count/Measured value without any context. So, that confused me a lot. This makes more sense. Thanks. $\endgroup$
    – ihateelectricalphysics
    Commented Mar 19, 2021 at 21:07

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