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The finest sextant verniers I've ever seen permit to read to 10 seconds accuracy. So when reading such a sextant it is natural to write the result in the format degrees, minutes, seconds. Drum sextants usually permit you to interpolate to 0.1 minute =6 seconds, and it is up to you to write the result is seconds or fractions of a minute. Sometimes they also have a vernier attached to the drum. More refined scales would be practically useless.

I understand that this is not what you meant when asking this question, but not all sextants were divided in degrees, minutes and fractions of a minute. There was a short period in France (after the French revolution) when decimal system was introduced for angle (and even time) measurements. The circle was divided to 400 decimal degrees, each decimal degree in 100 decimal minutes and each decimal minute into 100 decimal seconds. BTW, this explains the definition of kilometer: it is one decimal minute of the (Paris) meridian, similarly to the nautical mile which is one ordinary minute.

I've seen at least one such decimal sextant on e-bay.

Alex.