When someone says for example "We measured it to within 3%" Does this mean 3% is the percentage error?
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Depends...most of the time they would clarify whether or not it's error or what ever you're measuring. Is there more to this?
A lot of the times it's the error
Often we perform measurements of quantities that we do not know the exact value of.
Measurement techniques are not infinitely precise.
If a measurement determines the value a quantity to to be 100±3, then the relative percentage error in the measurement is 3%.
This mean that the true value is determined to be somewhere between 97 and 103.
The true value could be 100, in which case the percentage error is actually 0%.
But the true value could also be 103. In which case the actual percentage error is 3%.
From the measurement, the percentage error of the measured value can only be know to be less than or equal to 3%.
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No more. I listen to scientists talk. I hear them say for example we measured it to within 2%. I wonder if this "2%" just means percentage error. For example if the true mass of something is 5g and I measured it to be 4.7g, after calculating the percentage error which is 6%, can I say that I measured the mass to within 6%?
Ah gotcha, so yes in physics we say that it's \[\pm 0.03\] within the error, or percent, but percentage is often used in chem rather than physics hehe
Or put 3% depending on the measurement haha
As someone who's done quite a bit of error measurements/ calculations yup they mean \[\pm 3 \%\]