Wikipedia refers to the Julian Date system, which is used, primarily by astronomers, to this day. It is convenient due to irregularities in the standard calendar periods. The Julian days give a continuous count of days since the beginning of the Julian Period, introduced by Scaliger in 1583, i.e. since 1 January 4713 BC (Julian calendar), originally for the meridian of Alexandria. The Julian date (JD) is the Julian day number for the preceding mean noon in Universal Time plus the fraction of the day, the fraction is expressed in decimals. Here is an example from Ridpath's Oxford Dictionary of Astronomy (2012): 1962 June 24 at 18h UT is JD 2,437,840.25, and here is online Julian Date Converter.
Originally the Julian Period was used only to count years, and the Julian calendar was used to express days within years. Counting the days since the beginning was Herschel's innovation of 1849, in Outlines of Astronomy, the decimal fraction of the day addition was indeed Laplace's idea from Traité de Mécanique Céleste (1799). Another change, to the meridian of Greenwich instead of Alexandria, was made after its adoption as the Prime Meridian at the International Meridian Conference in Washington in 1884. Julian dates became standard practice after being adopted by Pickering, of the Harvard College Observatory, in 1890.