Fractional Days

A fractional day is the time of the day expressed as a decimal fraction. They can represent both time intervals (a period or length of time, such as, "I work 8 hours a day") or a time of the day (that is, the interval since midnight, such as, "I start work at 8 o'clock"). The time of day may be converted to the decimal fraction of the day by dividing the hours by 24, for example:
4:30 am = 4 hours 30 minutes = 4.5 hours = 4.5h/24h/d = 0.1875 day
This value may be represented by as many decimal places as necessary for precision. For example, 0.5 day (12 hours) can be written as 0.500 or 0.500000. However, three decimal places are usually sufficient to represent the time of day within one standard minute, and represent both Swatch .beats and French decimal minutes. Fractional days can be added to:
  • Calendar dates with fractional day of month (2004 June 29.286003)
  • Ordinal dates with fractional day of year (04181.286003)
  • Julian Dates (2453185.786003)
  • Implied dates with fraction of current day (0.286003 = 06:51:50.66)
Pierre-Simon Laplace, in his Traité de Mécanique Céleste, published in year VII of the Republican Calendar (1798), wrote, "I will adopt the decimal division of the right angle and of the day", and used the decimal fraction of the day to represent the time of day, e.g. 0j,60566. (The French word for "day" is jour, and the French decimal mark is a comma (,), while the British decimal mark was formerly a dot (·).)

After Laplace, other astronomers adopted fractional days. In 1849, John Herschel used fractional days to represent times of the day in his book, Outlines of Astronomy:
For example, at 12h 0m 0s Greenwich mean time, or 0d·500000... 0d·286003, or at 6h 51m 50s·66...

Calendar Dates

A fractional day can be added to the ordinal day of the month of Gregorian calendar dates.   Laplace may have been the first to do so, as when he wrote, "sept.29j,10239, temps moyen compté de minuit à Paris."  (In English, "mean time counted from midnight at Paris.")

Dates with fractional days may be found in astronomical circulars going back to the early 19th century. In the Journal of Astrophysics & Astronomy, published by the Indian Academy of Sciences, its Guidelines for Authors state:

   Miscellaneous: Following the recommendations of the IAU, the dates of observations, or of astronomical events, should be written in the order of year, month, day, so that in principle it can be appended by the decimal fraction of a day.
   e.g., a meeting was held in Delhi in January 1981 to discuss the results of the solar eclipse of 1980 February 16.

See also How to Submit Scientific Items for Publication in the IAUCs (International Astronomical Union Circulars):

...Give times to decimals of a day in Universal Time; use of JD is discouraged, but be sure to never use MJD. Dates should be given in the order YEAR MONTH DATE.

JPL Solar System Dynamics has a format for Small-Body Orbital Elements which includes:

Tp       Time of perihelion passage (comets only), formatted as a calendar date (YYYYMMDD.DDD) where "YYYY" is the year, "MM" is the numeric month, and "DD.DDD" is the day and day fraction.

This is consistant with the date order required by ISO 8601, but in astronomical usage the month is often referred to by full name or abbreviation than by number. The decimal time of day can then be appended to the ordinal day of the month as a decimal fraction, with as many decimal places as needed. For example, 12:00 PM January 1, 2000, is represented as 2000 Jan. 1.5 or 20000101.50000, which is the current standard epoch for celestial coordinates. This format is also often used to represent epochs of orbital elements for objects orbitting the sun or planets, perihelion dates, etc. The time scale is usually either Terrestrial Time or Universal Time, which may be indicated by the initials TT or UT, respectively. For more examples, see Dates Of Last Observation Of Comets.


Ordinal Dates

A fractional day can be added to the ordinal day of the year for ordinal dates. NASA and NORAD publish Two-Line Elements (TLE) for artificial satellites, which include epoch dates consisting of the epoch year followed by the epoch day, which is the ordinal day of the year (sometimes erroneously called "Julian date") with the epoch time added to the epoch day as a fractional day with eight decimal places. Leading zeros may or may not be present. For example, 12:00 January 1, 2000, is represented as 00  1.50000000 or 00001.50000000.


Decimal Dates

A fractional day can be added to a decimal date, which is a count of days from some epoch, such as a Julian Date, which vary according to when the day begins and ends.

Astronomical Time

Julian Date time is the fractional part of a Julian Date, which is 12 hours (0.5 day) behind Universal Time; that is, the fractional day is .0 around noon Greenwich Mean Time (GMT) and .5 around midnight. This is because when Julian Days were introduced the 19th century, astronomers then started and ended their days at noon, so the day in GMT originally started and ended at mean solar noon in Greenwich, while Greenwich Civil Time started at midnight. In 1925, GMT was changed to start at midnight, and the old GMT became called Greenwich Mean Astronomical Time (GMAT), which is twelve hours behind the new GMT (today called Universal Time). Julian Dates continue to be reckoned according to astronomical time, starting at noon, in order to remain consistent with older records. Terrestrial Time (TT) is now the officially recommended time scale, which is currently slightly more than a minute ahead of UT, in which case the Julian Date is 0.5 day (12 hours) behind TT, although UTC or other time scales may still be used.

Universal Time

Modified Julian Dates, and some other variations of Julian Dates, start and end around midnight GMT, so the fractional day is .0 at 00:00 UT, and .5 around noon GMT or 12:00 UT.

Local Time

Microsoft Excel uses a decimal date system called serial dates, which are similar to Julian Dates. Serial days begin and end with .0 at midnight local time, even during Daylight Saving Time, keeping in sync with the computer's clock year-round. Thus, two computers at different locations may have serial dates with different fractional values at the same instant.