Technically the shortness of note length has no limit. To make a note half as long, simply double the number it is named for. Notes longest to shortest are: whole note, half note, quarter note,...
It would depend on the note's date or series, its condition, and the fed branch to which it was issued, as well as potentially the serial number if it was and interesting one (eg "11111111" or...
It's value would depend on it's age and condition. An uncirculated example of the current issue note would be worth about $20. One from 1963 would be worth $135 or even $500 in uncirculated...