Confusing definition of the term precision
In colloquial English, precision is synonymous with accuracy. If you look it up on Google, the first definition is:


  the quality, condition, or fact of being exact and accurate.


In the field of science, however, it takes on another meaning:


  the degree to which repeated measurements under unchanged conditions show the same results


There is also measurement resolution:


  the smallest change [an instrument] can detect in the quantity that it is measuring


Which is similar to the definition precision takes on in numerical analysis:


  the resolution of the representation, typically defined by the number of decimal or binary digit


In short, precision can take on different meanings depending on how you choose to apply it. If you talk about the precision in a set of measured data, you will be using the scientific definition; if you talk about the precision of an instrument, you will be using the numerical analysis definition.