## Saturday, May 24, 2014

### [ugetibkd] Consistent subdivisions of a day

Here is what various units of time would be if the day were consistently divided as in base N, instead of the [24, 60, 60, 10, 10, ...] mixed radix system we use now:

1/30 day = 48 minutes
1/30^2 day = 1 minute 36 seconds
1/30^3 day = 3.2 seconds
1 hour = .01 07 15 day
1 minute = .00 00 18 22 15 day
1 second = .00 00 00 09 11 07 15 day

1/60 day = 24 minutes
1/60^2 day = 24 seconds
1/60^3 day = 0.4 seconds
1 hour = .02 30 day

1/10 day = 2 hours 24 minutes
1/10^2 day = 14 minutes 24 seconds
1/10^3 day = 1 minute 26.4 seconds
1/10^4 day = 8.64 seconds
1 hour = .04166... day
1 minute = .0006944... day
1 second = .0000115740740... day

1/2 day = 12 hours
...
1/2^4 day = 1 hour 30 minutes
...
1/2^10 day = 1 minute 24.375 seconds
...
1/2^16 day = 1.318359375 seconds
1 hour = .0000101... day
1 minute = .00000000001011011000001011011... day (30 bit repeat)
1 second = .0000000000000000110000100010111001000101000001100111001010001001010010101011011011001101100011101111101100010001110100110011111101010110000101111000001110011010010110111100011111011110101... day (180 bit repeat)