According to the textbook, we say a measurement is precise when series of measures are close to each other.
But in real use, I feel like the term is used in a different meaning.
For example, scale A weighs to cube of lead and displays 10.5g while scale B displays 10.4977g. In this case, one say the measurement made by scale B is more precise than that of A. That is, scale B can distinguish more fine weights than A.
Isn't this usage of the word precise different from textbook definition? Please explain clearly the real usage of the term precise.