As a first approximation, the uncertainty ($\delta X$) associated to a mensurand can be expressed as $\delta X= \Delta X / 2$ with $\Delta x$ being the resolution of the instrument.

There is also a recommendation indicating that the numerical expression of the result and its uncertainty saying that "Results should be rounded to be consistent with the uncertainty given" (EURACHEM/CITAC Guide CG 4).

So, if we have an instrument like a ruler with a resolution of 1 arbitrary unit ($\Delta X =1$ ) and when measuring an object, the end of said object is very close to the 3 unit mark, why should the reported value be 3 $\pm$ 0.5 and not 3.0 $\pm$ 0.5 or even 3.1 $\pm$ 0.5?

[![enter image description here][1]][1] [1]: https://i.sstatic.net/MH7I3.png

As a first approximation, the uncertainty ($\delta X$) associated to a mensurand can be expressed as $\delta X= \Delta X / 2$ with $\Delta x$ being the resolution of the instrument.

There is also a recommendation indicating that the numerical expression of the result and its uncertainty saying that "Results should be rounded to be consistent with the uncertainty given" (EURACHEM/CITAC Guide CG 4).

So, if we have an instrument like a ruler with a resolution of 1 arbitrary unit ($\Delta X =1$ ) and when measuring an object, the end of said object is very close to the 3 unit mark, why should the reported value be 3 $\pm$ 0.5 and not 3.0 $\pm$ 0.5 or even 3.1 $\pm$ 0.5?