I recommend your students read Daniel B. Delury's "Computations with
approximate numbers", _The Mathematics Teacher_, Vol. LI, No. 7, Nov.,
1958, pp.521-30; reprinted in _Precision Measurements and Calibration,
Selected NBS Papers on Statistical Concepts and Procedures_, Harry H.
Ku, Editor, NBS Special Publication 300 - Volume 1, February, 1969.
Delury notes: "Significant numbers are not good numbers to calculate
with, because the result of any computation with a significant number is
not a significant number... For this reason, people who take their
computations seriously do not use significant numbers, nor do they
necessarily state the results as significant numbers." (p. 523)