Quarters

Minutes were introduced to timekeeping with the first two-handed clocks. The word "minute" means small, as in a small part of an hour, and was copied from the minutes which divide degrees of angular measure, invented by the ancient Babylonians. The ancient sundials and the original one-handed clocks could only provide the precision of about a quarter of an hour. Quarter hours are still in frequent use today, when precision isn't required, and for a lot of scheduling use. One quarter is equal to about one-tenth of a decimal hour, or décime, or 10 minutes, 41.67 seconds decimal, to be exact. Below are the decimal times for every quarter-hour in one day. Décimes converted to decimal times are also available

24-hour Time	Decimal Time
00:00 = 12:00 am	0.0000 day = 0 h 0 m 0 s
00:15 = 12:15 am	0.0104 day = 0 h 10 m 41 s
00:30 = 12:30 am	0.0208 day = 0 h 20 m 83 s
00:45 = 12:45 am	0.0313 day = 0 h 31 m 25 s
01:00 = 1:00 am	0.0417 day = 0 h 41 m 66 s
01:15 = 1:15 am	0.0521 day = 0 h 52 m 8 s
01:30 = 1:30 am	0.0625 day = 0 h 62 m 50 s
01:45 = 1:45 am	0.0729 day = 0 h 72 m 91 s
02:00 = 2:00 am	0.0833 day = 0 h 83 m 33 s
02:15 = 2:15 am	0.0938 day = 0 h 93 m 75 s
02:30 = 2:30 am	0.1042 day = 1 h 4 m 16 s
02:45 = 2:45 am	0.1146 day = 1 h 14 m 58 s
03:00 = 3:00 am	0.1250 day = 1 h 25 m 0 s
03:15 = 3:15 am	0.1354 day = 1 h 35 m 41 s
03:30 = 3:30 am	0.1458 day = 1 h 45 m 83 s
03:45 = 3:45 am	0.1563 day = 1 h 56 m 25 s
04:00 = 4:00 am	0.1667 day = 1 h 66 m 66 s
04:15 = 4:15 am	0.1771 day = 1 h 77 m 8 s
04:30 = 4:30 am	0.1875 day = 1 h 87 m 50 s
04:45 = 4:45 am	0.1979 day = 1 h 97 m 91 s
05:00 = 5:00 am	0.2083 day = 2 h 8 m 33 s
05:15 = 5:15 am	0.2188 day = 2 h 18 m 75 s
05:30 = 5:30 am	0.2292 day = 2 h 29 m 16 s
05:45 = 5:45 am	0.2396 day = 2 h 39 m 58 s
06:00 = 6:00 am	0.2500 day = 2 h 50 m 0 s
06:15 = 6:15 am	0.2604 day = 2 h 60 m 41 s
06:30 = 6:30 am	0.2708 day = 2 h 70 m 83 s
06:45 = 6:45 am	0.2813 day = 2 h 81 m 25 s
07:00 = 7:00 am	0.2917 day = 2 h 91 m 66 s
07:15 = 7:15 am	0.3021 day = 3 h 2 m 8 s
07:30 = 7:30 am	0.3125 day = 3 h 12 m 50 s
07:45 = 7:45 am	0.3229 day = 3 h 22 m 91 s
08:00 = 8:00 am	0.3333 day = 3 h 33 m 33 s
08:15 = 8:15 am	0.3438 day = 3 h 43 m 75 s
08:30 = 8:30 am	0.3542 day = 3 h 54 m 16 s
08:45 = 8:45 am	0.3646 day = 3 h 64 m 58 s
09:00 = 9:00 am	0.3750 day = 3 h 75 m 0 s
09:15 = 9:15 am	0.3854 day = 3 h 85 m 41 s
09:30 = 9:30 am	0.3958 day = 3 h 95 m 83 s
09:45 = 9:45 am	0.4063 day = 4 h 6 m 25 s
10:00 = 10:00 am	0.4167 day = 4 h 16 m 66 s
10:15 = 10:15 am	0.4271 day = 4 h 27 m 8 s
10:30 = 10:30 am	0.4375 day = 4 h 37 m 50 s
10:45 = 10:45 am	0.4479 day = 4 h 47 m 91 s
11:00 = 11:00 am	0.4583 day = 4 h 58 m 33 s
11:15 = 11:15 am	0.4688 day = 4 h 68 m 75 s
11:30 = 11:30 am	0.4792 day = 4 h 79 m 16 s
11:45 = 11:45 am	0.4896 day = 4 h 89 m 58 s
12:00 = 12:00 pm	0.5000 day = 5 h 0 m 0 s
12:15 = 12:15 pm	0.5104 day = 5 h 10 m 41 s
12:30 = 12:30 pm	0.5208 day = 5 h 20 m 83 s
12:45 = 12:45 pm	0.5313 day = 5 h 31 m 25 s
13:00 = 1:00 pm	0.5417 day = 5 h 41 m 66 s
13:15 = 1:15 pm	0.5521 day = 5 h 52 m 8 s
13:30 = 1:30 pm	0.5625 day = 5 h 62 m 50 s
13:45 = 1:45 pm	0.5729 day = 5 h 72 m 91 s
14:00 = 2:00 pm	0.5833 day = 5 h 83 m 33 s
14:15 = 2:15 pm	0.5938 day = 5 h 93 m 75 s
14:30 = 2:30 pm	0.6042 day = 6 h 4 m 16 s
14:45 = 2:45 pm	0.6146 day = 6 h 14 m 58 s
15:00 = 3:00 pm	0.6250 day = 6 h 25 m 0 s
15:15 = 3:15 pm	0.6354 day = 6 h 35 m 41 s
15:30 = 3:30 pm	0.6458 day = 6 h 45 m 83 s
15:45 = 3:45 pm	0.6563 day = 6 h 56 m 25 s
16:00 = 4:00 pm	0.6667 day = 6 h 66 m 66 s
16:15 = 4:15 pm	0.6771 day = 6 h 77 m 8 s
16:30 = 4:30 pm	0.6875 day = 6 h 87 m 50 s
16:45 = 4:45 pm	0.6979 day = 6 h 97 m 91 s
17:00 = 5:00 pm	0.7083 day = 7 h 8 m 33 s
17:15 = 5:15 pm	0.7188 day = 7 h 18 m 75 s
17:30 = 5:30 pm	0.7292 day = 7 h 29 m 16 s
17:45 = 5:45 pm	0.7396 day = 7 h 39 m 58 s
18:00 = 6:00 pm	0.7500 day = 7 h 50 m 0 s
18:15 = 6:15 pm	0.7604 day = 7 h 60 m 41 s
18:30 = 6:30 pm	0.7708 day = 7 h 70 m 83 s
18:45 = 6:45 pm	0.7813 day = 7 h 81 m 25 s
19:00 = 7:00 pm	0.7917 day = 7 h 91 m 66 s
19:15 = 7:15 pm	0.8021 day = 8 h 2 m 8 s
19:30 = 7:30 pm	0.8125 day = 8 h 12 m 50 s
19:45 = 7:45 pm	0.8229 day = 8 h 22 m 91 s
20:00 = 8:00 pm	0.8333 day = 8 h 33 m 33 s
20:15 = 8:15 pm	0.8438 day = 8 h 43 m 75 s
20:30 = 8:30 pm	0.8542 day = 8 h 54 m 16 s
20:45 = 8:45 pm	0.8646 day = 8 h 64 m 58 s
21:00 = 9:00 pm	0.8750 day = 8 h 75 m 0 s
21:15 = 9:15 pm	0.8854 day = 8 h 85 m 41 s
21:30 = 9:30 pm	0.8958 day = 8 h 95 m 83 s
21:45 = 9:45 pm	0.9063 day = 9 h 6 m 25 s
22:00 = 10:00 pm	0.9167 day = 9 h 16 m 66 s
22:15 = 10:15 pm	0.9271 day = 9 h 27 m 8 s
22:30 = 10:30 pm	0.9375 day = 9 h 37 m 50 s
22:45 = 10:45 pm	0.9479 day = 9 h 47 m 91 s
23:00 = 11:00 pm	0.9583 day = 9 h 58 m 33 s
23:15 = 11:15 pm	0.9688 day = 9 h 68 m 75 s
23:30 = 11:30 pm	0.9792 day = 9 h 79 m 16 s
23:45 = 11:45 pm	0.9896 day = 9 h 89 m 58 s
24:00 = 12:00 am	1.0000 day = 10 h 0 m 0 s