Midnight to one hour

This birth certificate from the town of Russey in Doubs says:

Aujourd'hui quinze Nivose troisième année de la République une et indivisible à cinq heures décimales…le Jour d’hier quatorze du courant à quatre vingt trois minutes trente trois secondes du matin…

Today fifteen Nivose third year of the Republic one and indivisible at five decimal hours…yesterday, on the fourteenth day of the current (month) at eighty-three minutes thirty-three seconds in the morning…

83m 33s = 0.08333 days = 2:00 am, on January 3, 1795

Midnight was written as 𝒹𝒾𝓍 𝒽𝑒𝓊𝓇𝑒𝓈 𝒹𝑒𝒸𝒾𝓂𝒶𝓁𝑒𝓈. Times between midnight and the first decimal hour were written without the hours, that is; 

12:00 am = 10 hours decimal

1:00 am = 4 décimes or 41 minutes decimal

2:00 am = 8 décimes or 83 minutes decimal or 83 minutes 33 seconds decimal