Question

All measurements contain some error. Why is this a true statement?

Answer 1

You never can know the exact value of a physical or chemical dimension because several reasons:

all the instruments have a certain sensibility (sensibility is the smallest variation of the dimension that the instrument can measure) that cannot be overcame. (for example in a technical weight scale you cannot know smaller value than 0.01 g, and in an analytical weight scale one value smaller than 0.0001 g)

all the istruments have a certain imprecision (precision is the possibility to give the same value for the measure if you repeat it several times)

all the instruments aren't fully accurate (accuracy is the possibility of an instrument to give the exact value of the measure)