Suppose you had used a less sensitive balance for the archimedes method of getting volume of an object based on the difference in mass in water and out of water. would that change the precisions of your density for that method? . they define sensitivity as the scale to which things are measured and precision as how repeatable something is.

If you think about it, changing the scale to which something is measured does not affect the repeatability of the measurement. For instance, if you have a meter stick which was labeled incorrectly, that doesn't affect the fact that every measurement you take of a certain fixed distance will still be the same. Precision does not equal accuracy.