Question

What is the greatest possible error when measuring to the nearest quarter of an inch?

Answer 1

Length measurement accuracy (error) is always +/- `1/2` of the smallest calibrated measurement interval.

Explanation:

First, you must of course have a "calibrated" measurement device for any accuracy at all. Second, because anything smaller than the least calibrated distance on such a device can only be approximated by eye, the accuracy (or error) of the measured length can never be better than the approximate "middle" between the calibration marks.

You might make a claim to "see" the difference between `1/2 and 1/4` of the mark, but for scientific accuracy no such claim can really be justified as related to the required standard calibrated length.

Thus, if your calibration device (ruler, for example) is only calibrated to `1/4`-inch your error is +/-`1/8` inch. If it is only calibrated to one-inch intervals, the error in any measurement is +/-`1/2`-inch - much more than a quarter-inch.

However if your ruler is calibrated down to `1/32` inch intervals, your error would be only +/-`1/64`-inch.