The smallest unit of time that anybody outside of the worlds of physics, mathematics, and science is likely to use or even be aware of is the millisecond (one thousandth of a second) or perhaps the nanosecond (one billionth of a second).

These are used in exquisitely accurate clocks and for extremely fast races, while most ordinary races are timed in familiar units like hours, minutes, seconds, and tenths or hundreds of seconds.

The Attosecond (one quintillionth of a second) and Zeptosecond (one sextillionth of a second) are used to measure, for example, the motion of atomic particles and vibrations of molecules, which are useful in lasers and have opened entire new fields of study. At the extreme other end of the time spectrum, the yottasecond (one septillion seconds or 32 quadrillion years, far longer than the age of the universe) is used to define ages yet unrealized.

The Planck time unit—named after German physicist Max Planck, considered to be the founder of quantum physics—has been used to form a timeline to describe the events that occurred immediately after the Big Bang, and measures the shortest time interval that has any meaning at all (and, at that, only to theoretical physicians), 10 to the minus-43 seconds, which is called the "Planck Epoch."

More Info: en.wikipedia.org