Decimal time

French decimal clock from the time of the French Revolution

Decimal time is the representation of the time of day using units which are decimally related. This term is often used to refer specifically to French Revolutionary Time, which divides the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal seconds, as opposed to the more familiar standard time, which divides the day into 24 hours, each hour into 60 minutes and each minute into 60 seconds.

History

China

Main article: Ke (unit)

Decimal time was used in China throughout most of its history alongside duodecimal time. The midnight-to-midnight day was divided into both 12 double hours (Traditional Chinese: 時辰; Simplified Chinese: 时辰; Pinyin: shíchen) and 10 shi / 100 ke (Hanzi: 刻; Pinyin: kè) by the 1st millennium BC. Other numbers of ke per day were used during three short periods, 120 ke during 5–3 BC, 96 ke during 507–544, and 108 ke during 544–565. Several of the roughly 50 Chinese calendars also divided each ke into 100 fen, although others divided each ke into 60 fen. In 1280, the Shoushi (Season Granting) calendar further subdivided each fen into 100 miao, creating a complete decimal time system of 100 ke, 100 fen and 100 miao. Chinese decimal time ceased in 1645 when the Shixian (Constant Conformity) calendar, based on European astronomy brought to China by the Jesuits, adopted 96 ke per day alongside 12 double hours, making each ke exactly one-quarter hour.

France

In more modern times, decimal time was introduced during the French Revolution in the decree of 5 October 1793:

XI. Le jour, de minuit à minuit, est divisé en dix parties, chaque partie en dix autres, ainsi de suite jusqu’à la plus petite portion commensurable de la durée.

XI. The day, from midnight to midnight, is divided into ten parts, each part into ten others, so on until the smallest measurable portion of duration.

These parts were named on 24 November 1793 (4 Frimaire of the Year II). The primary divisions were called hours, and they added:

La centième partie de l'heure est appelée minute décimale; la centième partie de la minute est appelée seconde décimale. (emphasis in original)

The hundredth part of the hour is called decimal minute; the hundredth part of the minute is called decimal second.

Thus, midnight was reckoned as 10 o'clock, noon as 5 o'clock, etc. Although clocks and watches were produced with faces showing both standard time with numbers 1–24 and decimal time with numbers 1–10, decimal time never caught on; it was not officially used until the beginning of the Republican year III, 22 September 1794, and mandatory use was suspended 7 April 1795 (18 Germinal of the Year III), in the same law which introduced the original metric system. Thus, the metric system at first had no time unit, and later versions of the metric system used the second, equal to 1/86400 day, as the metric time unit.

Decimal time was introduced as part of the French Republican Calendar, which, in addition to decimally dividing the day, divided the month into three décades of 10 days each; this calendar was abolished at the end of 1805. The start of each year was determined according to which day the autumnal equinox occurred, in relation to true or apparent solar time at the Paris Observatory. Decimal time would also have been reckoned according to apparent solar time, depending on the location it was observed, as was already the practice generally for the setting of clocks.

The French made another attempt at the decimalization of time in 1897, when the Commission de décimalisation du temps was created by the Bureau des Longitudes, with the mathematician Henri Poincaré as secretary. The commission proposed a compromise of retaining the 24-hour day, but dividing each hour into 100 decimal minutes, and each minute into 100 seconds. The plan did not gain acceptance and was abandoned in 1900.

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 are 100,000 decimal seconds in the day, so the decimal second is shorter than its counterpart.

Decimal unit	Seconds	Minutes	Hours	h:mm:ss.s
Decimal second	0.864	0.0144	0.00024	0:00:00.9
Decimal minute	86.4	1.44	0.024	0:01:26.4
Decimal hour	8,640	144	2.4	2:24:00.0

Fractional days

The most common use of decimal time of day is as fractional days used by scientists and computer programmers. Standard 24-hour time is converted into a fractional day simply 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:

• Gregorian dates: 2000 January 1.5
• ordinal dates: 00001.5
• 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 reckoned in UTC or TT, although Julian Dates use pre-1925 astronomical date/time (each date began at 0^h thus ".0" = noon) 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 in his book, Traité de Mécanique Céleste, as in these examples:

... et la distance périhélie, égale à 1,053095 ; ce qui a donné pour l'instant du passage au périhélie, sept.29^j,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.29^j,04587; ce qui diffère peu des résultats fondés sur cinq observations.

Fractional days were later used by the 19th century British astronomer John Herschel in his book, Outlines of Astronomy, as in 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 0^d·286003, or at 4^h 51^m 50^s·66 Greenwich Mean Time ... For example, at 12^h 0^m 0^s Greenwich Mean Time, or 0^d·500000...

Fractional seconds are arguably more used than fractional days in practice. This is the standard single-unit time representation in many programming languages, most notably C, and part of UNIX/POSIX standards used by Mac OS X, Linux, etc.; to convert fractional days to fractional seconds, multiply the number by 86400. Absolute times are usually represented relative to 1 January 1970, at midnight. Other systems may use a different zero point, may count in milliseconds instead of seconds, etc.

In practice, most of the time, neither fractional days nor fractional seconds are expressed in decimal, because almost all computer representations of fractional time are made using binary coding. Decimal is sometimes but rarely used for computation, more often for storage, but never as much as for human interaction.

Decimal multiples of the SI second

In the International System of Units (SI), in principle, time spans greater than one second are 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 hours, days and years are much more common.

It is possible to specify the time of day as the number of kiloseconds elapsed 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. However, this system is hardly used in practice.

Scientific decimal time

Scientists often record (rather than observe) time as decimals. For example, decimal days divides the day into 10 equal parts, and decimal years divides the year into 10 equal parts. Decimals are easier to plot than both (a) minutes and seconds, which uses the Sexagesimal numbering system, (b) hours, months and days, which has irregular month lengths. In astronomy, the so-called Julian Day uses decimal days centered on noon.

Decimal minutes

Since there are 60 seconds in a minute, a tenth part represents 60/10 = 6 seconds.

Conversion between decimal minutes seconds
Decimal Minutes	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
Second	6s	12s	18s	24s	30s	36s	42s	48s	54s	60s

Decimal hours

Since there are 60 minutes in an hour, a tenth part represents 60/10 = 6 minutes.

Conversion between decimal hours and minutes
Decimal Hours	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
Minutes	6m	12m	18m	24m	30m	36m	42m	48m	54m	60m

Decimal days

Since there are 24 hours in a day, a tenth part represents 24/10 = 2.4 hours (2 hours and 24 minutes).

Conversion between decimal day, and, Hours and minutes
Decimal Days	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
Hours:Minutes	2h 24m	4h 48m	7h 12m	9h 36m	12h	14h 24m	16h 48m	19h 12m	21h 36m	24h

Decimal years

Since there are about 365 days in a year, there are about 365/10 = 36.5 days in a tenth of a year. Hence the year 2000.5 represents the day 2 July 2000. More exactly, a year is 365.25 days long, so a tenth of the year is 36.525 days (36 days, 12 hours, 36 minutes).

Conversion between decimal years, and, Date
Decimal Years	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
Days	36.525	73.050	109.575	146.100	182.625	219.150	255.675	292.200	328.725	365.250
Date Time	5 Feb 12:36	14 Mar 1:15	19 Apr 13:48	26 May 2:24	1 Jul 15:00	7 Aug 3:45	12 Sep 16:12	19 Oct 4:48	24 Nov 17:24	1 year

In leap years, all days after 28 Feb occur one day earlier

Other decimal times

Numerous individuals have proposed variations of decimal time, dividing the day into different numbers of units and subunits with different names. Most are based upon fractional days, so that one decimal time format may be easily converted into another, such that all the following are equivalent:

• 0.500 fractional day
• 5h 0m French decimal time
• @500 Swatch Internet Time (see below)
• 50.0 centidays
• 500 millidays
• 50.0% Percent Time
• 12:00 Standard Time

Some decimal time proposals are based upon alternate units of metric time. The difference between metric time and decimal time is that metric time defines units for measuring time interval, as measured with a stopwatch, and decimal time defines the time of day, as measured by a clock. Just as standard time uses the metric time unit of the second as its basis, proposed decimal time scales may use alternative metric units.

Swatch Internet Time

Main article: Swatch Internet Time

On 23 October 1998, the Swiss watchmaking company, Swatch, introduced a decimal time called Swatch Internet Time, which divides the day into 1000 .beats (each 86.4 s) counted from 000–999, with @000 being midnight and @500 being noon CET (UTC +1), as opposed to UTC. The company sold watches which displayed Internet Time.

Internet Time has been criticized for using an origin different from Universal Time, misrepresenting CET as "Biel Mean Time", and for not providing for more precise units, although third-party applications have proposed "centibeats" (864 ms) and "millibeats" (86.4 ms).

Decimal times in fiction

Some science fiction authors use decimal time to reinforce the sense of "otherworldliness", notably in Infocom's Planetfall and Stationfall games, which use "1 chronon = 1/10000 day" such that 0000 = midnight and 5000 = noon.

Isaac Asimov also uses and describes the use of decimal time by the humans from the planet Solaria in his novel The Naked Sun, in which he describes the Solarian hour as being divided into ten decads, each of which is divided into a hundred centads.

Vernor Vinge's A Fire Upon the Deep and A Deepness in the Sky include human cultures that base time on seconds and multiples of seconds, with one "kilosecond" equal to 1,000 seconds (or approximately 15 minutes), one "megasecond" equal to 1,000,000 seconds (or approximately two weeks), and one "gigasecond" equal to 1,000,000,000 seconds (or approximately 30 years).

Greg Bear's Anvil of Stars tells the story of a starship crew that structure their calendar in "tendays" instead of weeks. Tendays are also mentioned in Diane Duane's The Wounded Sky.

Fritz Lang's science fiction film Metropolis depicts what is often misinterpreted as a decimal clock, as it has ten numerals, but it actually measures a workers' shift of ten conventional hours in one cycle, not decimal hours^{[citation needed]}. Since a normal day cannot be divided into a whole number of such shifts, a 24-hour clock is displayed above the shift clock to give the actual time of day.

In the episode of The Simpsons, "They Saved Lisa's Brain", the members of Springfield's Mensa make changes to their town, including the implementation of using "metric time" to determine the time of day. Dr. Hibbert comments that the time is "eighty past ten". Using "metric time" to indicate decimal time, Principal Skinner comments that the city's trains are not only running on time, but they are running on metric time, while looking at an analog clock with numbers 1–10.

In the original Battlestar Galactica television series, both the Colonials and the Cylon Alliance employed a decimal time system. An are was an equivalent of an hour but was nearly twice as long. A centon was 1/100th of an are, in the same order of magnitude as a minute. A micron [sic] was 1/1000 of an are, on the same order of magnitude as a second. A centare was 100 are units and represented the same order of magnitude of time as a week. A yahren was 100 centare units and represented the same order of magnitude as a year. Usage of these terms was not always consistent. In the pilot, "Saga of a Star World," Lew Ayres as President Adar used the term "years." And occasionally, the terms above were used inconsistently, or other time terms were used in place of those listed above which seemed to be the same as one of those defined above. (e.g. - Secton)

The Warhammer 40,000 science fiction wargame universe uses a dating system that includes a year fraction, dividing the year into 1,000 equal parts (just over 8 hours each). Dates include an optional accuracy specifier, year fraction, year, and millenium so you see dates like 0123456.M41, which would be the decimal year 40456.123 with an accuracy of 0 (on earth).

See also

• Decimal calendar
• Hexadecimal time
• List of unusual units of measurement
• Stardate
• Unix time
• 24-hour clock

References

• National Convention of the French Republic (1793) LE CALENDRIER RÉPUBLICAIN Textes officiels Décrets Relatifs à l'établissement de l'Ère Républicaine published by Philippe Chapelin 2002
• Sizes, Inc. (2000) decimal time units Last revised 27 February 2004
• Herschel, John (1849) Outlines of Astronomy published by Gallica 1995
• Carrigan, Richard A., Jr. "Decimal Time". American Scientist, (May–June 1978), 66(3): 305–313.

External links

• Live Decimal Time as per your PC clock.
• Decimal Time Applet - with digital and analogue representations.
• What DIME is it? (Dime = Decimal Time) (Decimal time Java applet by Sergey Zaitsev.)
• Revolutionary Time
• Dials & Symbols of the French revolution. The Republican Calendar and Decimal time.