Q.Your laboratory partner was given the task of measuring the length of a box (approx 5 in) as accurately as possible, using a metre stick graduated in milimeters. He supplied you with the following measurements: 12.65 cm, 12.6 cm, 12.65 cm, 12.655 cm, 126.55 mm, 12 cm. a. State which of the measurements you would accept, giving the reason. (Ans.: 12.6 cm) b. Give your reason for rejecting each of the others.

a. Which to accept. The metre stick's least count is 1 mm = 0.1 cm, so by the chapter's own convention (illustrated for the burette in section 2.3.2), a correctly reported reading has ONE decimal place in cm, with that last digit being the reading taken directly at the smallest graduation. 12.6 cm has exactly one decimal place, matching the instrument's least count, so it is the reading to accept.

b. Reasons for rejecting the others. 12.65 cm (appearing twice) and 12.655 cm both carry more decimal places than the 1 mm graduations justify — reading '12.65' or '12.655' implies the ruler could resolve to 0.01 cm or 0.001 cm, which it cannot; these are OVER-PRECISE. 126.55 mm is the same value as 12.655 cm in different units, and is rejected for the same over-precision reason (it implies resolving to 0.01 mm). 12 cm, with no decimal place at all, only claims precision to the nea …

Compare the number of decimal places (in cm) each reading carries against the metre stick's least count (1 mm = 0.1 cm, i.e. one decimal place in cm), following the same significa …

• Accepting a more 'precise-looking' reading like 12.655 cm simply because it has more decimal digits, without checking whether the instrument can actually justify that many. …