While Pennie1478's description of the zeptosecond is correct, it is not the shortest time interval for which a name has been adopted, for the moment (all that is needed is for someone to propose a shorter interval) that appears to be the yoctosecond, a fraction of a second represented by a decimal point followed by 23 zeroes and a one. In the short form enumeration favored in the United States the yoctosecond is one septillionth of a second. In the long form enumeration used in Europe it is one quadrillionth of a second.
While Pennie1478's description of the zeptosecond is correct, Jdeanflpa's response could be discussed since there is a so called "Planck Time" - by definition the time required for light to travel a distance of 1 Planck length in a vacuum, a time interval of approximately 5.39×10 to the power of ?44 of a second (thus the 100,000,000,000,000,000,000th part of a zeptosecond).
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