# “The mass of the proton is $1.672\,621\,637(83) \times 10^{-27}\:\mathrm{kg}$” - please, how does the error work for this? [duplicate]

Sorry if this is a basic question, but I just want to be sure about this because I am doing some research. I have never been sure what the number in brackets means in scientific values like this.

$$1.672\,621\,637(83) \times 10^{-27}\:\mathrm{kg}$$

In this example, would this mean that the maximum is $1.672\,621\,720 \times 10^{-27}\:\mathrm{kg}$ and the minimum is $1.672\,621\,554 \times 10^{-27}\:\mathrm{kg}$ ?

Could this also be written $1.672\,621\,637\times 10^{-27} \pm 0.000\,000\,083 \times 10^{-27}\:\mathrm{kg}$?

## 1 Answer

Could this also be written 1.672 621 637 x 10 -27 +/- 0.000 000 083 x 10 -27 kg ?

Yes.

In this example, would this mean that the maximum is 1.672 621 720 x 10 -27 kg and the minimum is 1.672 621 554 x 10 -27 kg ?

No. The uncertainty is usually given as standard deviation of a mean value. That means that the true value falls within the given uncertainty range about 68.3 % of the time. (The 68.3 % correspond to the integral from -1 standard deviation to +1 standard deviation of the normal distribution). There is still a sizable probability that the true value lies outside the given range!