(Note: A "new" hour/minute/second is how long an hour/minute/second would be in this case, and a "normal" hour/minute/second is how long an hour/minute/second actually is.
NMH = Normal Hour
NWH = New Hour
NMM = Normal Minute
NWM = New Minute
NMS = Normal Second
NWS = New second)
The best way to solve this would be to see how long an hour would be in normal minutes, then how long a minute would be in normal seconds, then how long a second would be in normal seconds.
A day would be 24 normal hours and 100 new hours, so if NMH stands for Normal Hours, and NWH stands for New Hours, then
24 x NMH = 100 x NWH
One could replace Normal Hours with 60 Normal Minutes (NMM), soooo
24 x (60 x NMM) = 100 x NWH
Multiply 24 and 60
1440 NMM = 100 x NWH
Divide by 100 and you get
14.4 NMM = NWH
Or
1 New Hour = 14.4 Normal Minutes.
The next step is to solve for New Minutes (NWM)
Since a New Hour (NWH) has 14.4 Normal Minutes and 100 New Minutes (NWM),
14.4 x NMM = 100 NWM
A Normal Minute (NMM) is 60 Normal Seconds (NMS), so
14.4 x (60 x NMS) = 100 NWM
Multiply 14.4 by 60 and get
864 x NMS = 100 x NWM
Divide by 100 and get
8.64 NMS = NWM
Or
1 Normal Minute = 8.64 Normal Seconds.
Now, a New Minute (NWM) is 100 New Seconds (NWS), so
1 NWM = 100 NWS
A New Minute is 8.64 Normal Seconds (NMS) so
8.64 NMS = 100 NWS
Divide by 100 and get
0.0864 NMS = 1 NWS
Or
1 New Second = 0.0864 Normal Seconds.
There you have it, if there are 100 hours in a day, a 100 minutes in an hour, and 100 seconds in a minute, but days are still the same length as before, then a second would be 0.0864 normal seconds, or 86.4 milliseconds.
Here is the new time system:
1 second = 1 second (86.4 normal milliseconds)
1 Minute = 100 seconds (8.64 normal seconds)
1 Hour = 100 Minutes (14.4 Normal Minutes)
1 Day = 100 Hours (The time it takes for Earth to rotate once)
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