One sidereal period of the earth is 365.25 days; 100 of them is 36525 days. One millionth of that amount is 0.036525 days. Since a day is defined to be (24hr * 60min/hr) 1440 minutes long, the number of minutes in a microcentry is 0.036525 * 1440 = 52.596 minutes. The .596min still needs conversion to seconds (.596 min * 60 s/min), 35.76s.

A microcentury is 52 min 35.76 sec long. However I wasn't keeping track of significant digits very carefully (it varied between 5 and 6) so I'd take the "6" with a grain of salt pending further analysis.