# What is meant by precision?

I've found two different meanings of precision:

Meaning 1 (from Grade 11 Physics textbook,India):

Precision tells us to what resolution or limit a quantity is measured.

Meaning 2 (from Grade 11 Chemistry Textbook,India):

Precision refers to the closeness of various measurements for the same quantity.

It's really confusing to have two different meanings for the same term. I think, textbooks can't be wrong. Does this mean that precision in physics is different from precision in chemistry?

• Precision is about repeatability which is how similar repeated measurements read to each other (different from accuracy since you can have measurements that are very inaccurate but very repeatable), so the first definition don't seem quite right, especially the first. At least, the first definition doesn't seem to differentiate from resolution associated with precision vs resolution associated with accuracy. Aug 6, 2021 at 15:19
• Coincidentally, I posted pretty much the same contrast one day before you. Mar 28, 2022 at 18:41

The first definition refers to the precision of a single measurement, whereas the second refers to the precision of a group of measurements.

Suppose I have a digital stopwatch that measures time in seconds with three decimal places. If I make one measurement of the period of a pendulum I will get a value that has a precision of one thousandth of a second. If I make ten measurements of the period of the same pendulum then those measurements could be spread over a range of one tenth of a second or more - the limiting factor is now my reaction time, not the precision of the stopwatch. Note that we have said nothing so far about the accuracy of the measurements - if the stopwatch is faulty then they may be precise but very inaccurate.

Not at all. Those definitions of precision do not have opposite meanings, just different. The first one refers to the number of digits a given measured quantity can have (its resolution). For example, the speed of light in vacuum is measured to be:

$$c = 299\,792\,458 \rm\, m/s$$

Which is precise to the 9th digit. Other experimentally measured quantities may have different precisions like the mass of the electron, which precision or resolution offers 2 more digits.

$$m_{e} = 9.109\,383\,7015 \times 10^{-31}\rm\, kg$$

The second meaning you've found is related to a different aspect of precision. If you perform an experiment whose outcome is one quantity, you may perform it again and again some number of times $$n$$. If each result from each experiment is close together with the remaining ones, then the overall result is said to be precise. If they are not, meaning that they are spread out, then the overall result is imprecise.

• The speed of light in vacuum is now defined to be 299 792 458 m/s exactly. It doesn't make sense to say that it is "precise to the 9th digit" or that it is "experimentally measured." Aug 6, 2021 at 15:26
• ...And in the second case the closer the repeated results are to each other the more confident you can be about expressing the result with a greater number of digits. Aug 6, 2021 at 15:27
• Ok! Thank you for the feedback. But is the value of the speed of light theoretically predicted? Aug 6, 2021 at 15:31
• We have collectively (via the BIPM) decided to use a particular kind of cesium clock to define the second, and to use the speed of light plus this clock to define the meter. The theoretical prediction is that this choice is valid in all inertial reference frames. You might enjoy this question and answer, and links therein.
– rob
Aug 6, 2021 at 15:44

Accuracy is the degree of closeness of readings to the value relative to an agreed standard.

Precision is the closeness of the measurements to each other.

I like this sort of image when differentiating between precision and accuracy. The true value is the centre of the target.

A 101 cm long rule with calibration marks indicating that it is one metre long will produce readings of length with approximately the same precision as a metre rule which is one metre long as compared to the SI definition as the metre, but will not be as accurate.

The inaccurate rule will measure an accurately measured length of 100 cm as 99 cm.