Decimal System

Pure decimal system for date and time, that correlated with solar events, does not exist.
The pure system will have all the units (seconds, minutes, hours, days, weeks, months, years) with factor 10.

That will not match solar astrological events.

First real attempt to introduce a decimal time was as part of French Republican calendar.

In 1788, Claude Boniface Collignon proposed dividing the day into 10 hours or 1000 minutes, each new hour into 100 minutes, each new minute into 1000 seconds, and each new second into 1000 tierces (Latin for "third").

Decimal time was officially introduced during the French Revolution and used for about 12 years from late 1793 to 1805

The week was decimalized (10 days), but the month was 30 days, year 12 months, and extra 5 days which is not belonged to any month.

The 10-day week was unpopular with laborers because they received only one full day of rest out of ten, instead of one in seven.

Date and time wasn't unified as one system.

Even though these calendars are not decimal, there was plenty of proposals to make a perennial calendar:

• Hanke–Henry Permanent Calendar

• International Fixed Calendar

• Blank-day calendars

• Leap-week calendars

• World Calendar

First four digits correspond to the year, while the remainder was intended to stand for the day of the year. In the first installment of the movie trilogy, Spock makes his log of the destruction of Vulcan on stardate 2258.42, or February 11, 2258. Star Trek Into Darkness begins on stardate 2259.55, or February 24, 2259. Star Trek Beyond begins on stardate 2263.02, or January 2, 2263.

Excel, in Microsoft Office, uses it's own calendar - Excel Date-Time. It counts past days and decimal fractions of days.
The underlying data type of a datetime in Excel is a 64-bit floating point number where the length of a day equals 1 and 1st Jan 1900 00:00 equals 1. So 11th June 2009 17:30 is about 39975.72917
This format is not counting years as seasonal events.

The unix time stamp is a way to track time as a running total of seconds. This count starts at the Unix Epoch on January 1st, 1970 at UTC. Therefore, the unix time stamp is merely the number of seconds between a particular date and the Unix Epoch.

Example:

common date  =>  Unix Timestamp
April 15, 2022 => 1650063885

The centiday, (called kè in Chinese) was used in China for thousands of years. One kè was usually defined as 1⁄100 of a day 

Swatch Internet Time (or .beat time) is a decimal time concept introduced in 1998 by the Swatch corporation as part of their marketing campaign for their line of "Beat" watches.

Instead of hours and minutes, the mean solar day is divided into 1000 parts called .beats. Each .beat is equal to one decimal minute in the French Revolutionary decimal time system and lasts 1 minute and 26.4 seconds (86.4 seconds) in standard time. Times are notated as a 3-digit number out of 1000 after midnight. So, for example @248 would indicate a time 248 .beats after midnight representing 248⁄1000 of a day, just over 5 hours and 57 minutes.

A very good attempt to improve French Republican system was made in C10 system. 

The main Idea:

Year and day are the same as astrological events.

1 day = 100 intervals (the equivalent of 'hours')

1 interval = 100 centivals (equivalent of 'minutes')

1 centival = 100 ticks (equivalent of 'seconds')

1 tick = 0.0864 current seconds

If the year is an odd number it will be a 'leap' year and have 37 decades. 'Normal' years will have 36 decades. This means every second year in row will be a leap year. 

The date starts 1/1

Months are obsolete, as it represent moon cycles.

Read more

• The logic of Date system and time system is different. Date is counted as an “ongoing” system as opposed to time that counts as “time past” system. Nobody ever questioned this logic.

• None of these systems can be written in real decimal string (even without the year number)

• All the calendars starting to count from some random year/date. Even in Gregorian calendar 2022 doesn't mean that Jesus was born 2022 years ago (not to mention the start of the year - January 1st)

UDATE system is improving C10 system.

Months are resurrected, not as a moon cycles, but as a season of the year.

Logic of dates is changed, to match in one decimal string with time (now it's truly one system).

Year number is absolute (does not start with random date)