What is the smallest unit of time?
Unit of time
Sun based: the year was the time for the earth to rotate around the sun. Year-based units include the olympiad (four years), the lustrum (five years), the indiction (15 years), the decade, the century, and the millennium.
Moon based: the month was based on the moon's orbital period around the earth.
Earth based: the time it took for the earth to rotate on its own axis, as observed on a sundial. Units originally derived from this base include the week at seven days, and the fortnight at 14 days. Subdivisions of the day include the hour (1/24th of a day) which was further subdivided into minutes and finally seconds.  The second became the international standard unit (SI units) for science.
Celestial sphere based: as in sidereal time, where the apparent movement of the stars and constellations across the sky is used to calculate the length of a year.