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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Decimal time | 4/5 | https://en.wikipedia.org/wiki/Decimal_time | reference | science, encyclopedia | 2026-05-05T11:12:32.390542+00:00 | kb-cron |
On 23 October 1998, the Swiss watch company Swatch introduced a decimal time called Internet Time for its line of digital watches, which divided the day into 1,000 ".beats", (each 86.4 seconds in standard time) counted from 000–999, with @000 being midnight and @500 being noon standard time in Switzerland, which is Central European Time (one hour ahead of Universal Time). Although Swatch did not specify units smaller than one .beat, third party implementations extended the standard by adding "centibeats" or "sub-beats", for extended precision: @248.00. Each "centibeat" was a hundredth of a .beat and was therefore equal to one French decimal second (0.864 seconds). When using .beats and centibeats, Swatch Internet Time divided the day into 1,000 French decimal minutes and each decimal minute into 100 decimal seconds. So 9pm was 21:00:00 in standard time and @875.00 in extended Swatch Internet Time. Swatch no longer markets digital watches with Internet Time.
== Conversions == There are exactly 86,400 standard seconds (see SI for the current definition of the standard second) in a standard day, but in the French decimal time system there were 100,000 decimal seconds in the day; thus, the decimal second was 13.6% shorter than its standard counterpart.
== Decimal hours ==
Another common type of decimal time is decimal hours. In 1896, Henri de Sarrauton of the Oran Geographical Society proposed dividing the 24 hours of the day each into 100 decimal minutes, and each minute into 100 decimal seconds. Although endorsed by the Bureau des Longitudes, this proposal failed, but using decimal fractions of an hour to represent the time of day instead of minutes has become common. Decimal hours are frequently used in accounting for payrolls and hourly billing. Time clocks typically record the time of day in tenths or hundredths of an hour. For instance, 08:30 would be recorded as 08.50. This is intended to make accounting easier by eliminating the need to convert between minutes and hours. For aviation purposes, where it is common to add times in an already complicated environment, time tracking is simplified by recording decimal fractions of hours. For instance, instead of adding 1:36 to 2:36, getting 3:72 and converting it to 4:12, one would add 1.6 to 2.6 and get 4.2 hours.
== Fractional days == The time of day is sometimes represented as a decimal fraction of a day in science and computers. Standard 24-hour time is converted into a fractional day by dividing the number of hours elapsed since midnight by 24 to make a decimal fraction. Thus, midnight is 0.0 day, noon is 0.5 d, etc., which can be added to any type of date, including the following, all of which refer to the same moment in time:
Gregorian dates: 2000 January 1.5 Two-line elements: 00001.50000000 Julian dates: 2451545.0 Excel serial dates: 36526.5
As many decimal places may be used as required for precision, so 0.5 d = 0.500000 d. Fractional days are often calculated in UTC or TT, although Julian Dates use pre-1925 astronomical date/time (each date began at noon = ".0") and Microsoft Excel uses the local time zone of the computer. Using fractional days reduces the number of units in time calculations from four (days, hours, minutes, seconds) to just one (days). Fractional days are often used by astronomers to record observations, and were expressed in relation to Paris Mean Time by the 18th century French mathematician and astronomer Pierre-Simon Laplace, as in these examples:
... et la distance périhélie, égale à 1,053095; ce qui a donné pour l'instant du passage au périhélie, sept.29j,10239, temps moyen compté de minuit à Paris.
Les valeurs précédentes de a, b, h, l, relatives à trois observations, ont donné la distance périhélie égale à 1,053650; et pour l'instant du passage, sept.29j,04587; ce qui diffère peu des résultats fondés sur cinq observations. Fractional days have been used by astronomers ever since. For instance, the 19th century British astronomer John Herschel gave these examples:
Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 0d·286003, or at 6h 51m 50s·66 Greenwich Mean Time ... For example, at 12h 0m 0s Greenwich Mean Time, or 0d·500000... Fractional days are commonly used to express epochs of orbital elements. The decimal fraction is usually added to the calendar date or Julian day for natural objects, or to the ordinal date for artificial satellites in two-line elements.
== Decimal multiples and fractions of the second == The second is the International System of Units (SI) unit of time duration. It is also the standard single-unit time representation in many programming languages, most notably C, and part of UNIX/POSIX standards used by Linux, Mac OS X, etc.; to convert fractional days to fractional seconds, multiply the number by 86400. Fractional seconds are represented as milliseconds (ms), microseconds (μs) or nanoseconds (ns). Absolute times are usually represented relative to 1 January 1970, at midnight UT. Other systems may use a different zero point (like Unix time). In principle, time spans greater than one second may be given in units such as kiloseconds (ks), megaseconds (Ms), gigaseconds (Gs), and so on. Occasionally, these units can be found in technical literature, but traditional units like minutes, hours, days and years are much more common, and are accepted for use with SI. It is possible to specify the time of day as the number of kiloseconds of elapsed time since midnight. Thus, instead of saying 3:45 p.m. one could say (time of day) 56.7 ks. There are exactly 86.4 ks in one day (each kilosecond being equivalent to 16 minutes and 40 seconds worth of conventional time). However, this nomenclature is rarely used in practice.