The entry would be 30.4160, i.e. degrees separated from minutes by a decimal point. Minutes are whole minutes and then tenths and hundredths.
For example, 30 deg 4.65 minutes would be entered 30.0465.
Frankly the extra precision really doesn't add a lot to the process. You're generally looking at one minute per mile and most people can't get a sextant reading from the deck of a small boat that's more reliable then one minute. With lots of practice maybe .5 minutes. For star sights with a good horizon and 3 stars about the best an experienced person can do is about 1000 yards of an actual position. Sometimes better but usually not. With good conditions I generally assume my circle of error is about a mile or so in radius which is usually close enough.
Cheers,
s/v HyLyte