25.4 exactly
One inch is defined as exactly 25.4 millimetres, which follows directly from the 1959 definition of the inch as 2.54 cm. Because the factor is exact, converting between the two systems introduces no error at all — every millimetre figure has a precise inch equivalent and vice versa. What introduces error is the rounding you do afterwards.
Sixty-fourths, sixteenths and thousandths
Imperial workshops divide the inch in two different ways depending on the trade. Carpentry and general fabrication use binary fractions down to a sixteenth or a sixty-fourth, because that is how rules and drill sets are marked. Machining abandons fractions entirely and works in thousandths of an inch — a “thou” or “mil” — because a lathe dial is graduated decimally.
The page gives you all three. The note under the results tells you how much you actually lose by rounding to the nearest sixty-fourth, which is at most about 0.2 mm. If that matters, use the decimal or the thou figure instead.
Where this catches people out
Metric and imperial fastener sizes are close enough to be dangerous. A 10 mm bolt is 0.3937 inches, which is not quite 3/8″ (0.375″) and not quite 13/32″ (0.40625″). A 13 mm spanner will sit on a 1/2″ nut with 0.3 mm of slop — enough to round the corners under load. The usable near-matches are few: 25.4 mm is exactly one inch, and 12.7 mm is exactly half of one.