It means the same as 19:45 or 7:45PM
There seems to be several elements in the original text that are confusing.
At approximately 19.45 hours...
The dot in the time notation is not a decimal point, as in "19 point 45", as in 45 hundredths of an hour. It's an alternative to the colon as the time separator and would be pronounced "nineteen forty five hours".
There are a variety of names for the "dot" symbol, but this one would be a "full stop" or a "period". Both terms are equivalent and are used in Commonwealth English and American English respectively.
Many languages use a dot as a separator between hours, minutes and seconds. In Germany, it was the standard notation up until 1996 and is still commonly seen.
The German standard DIN 5008, which specifies typographical rules for German texts written on typewriters, was updated in 1996-05. The old German numeric date notations DD.MM.YYYY and DD.MM.YY have been replaced by the ISO date notations YYYY-MM-DD and YY-MM-DD. Similarly, the old German time notations hh.mm and hh.mm.ss have been replaced by the ISO notations hh:mm and hh:mm:ss. Those new notations are now also mentioned in the latest edition of the Duden. The German alphanumeric date notation continues to be for example “3. August 1994” or “3. Aug. 1994”.
It is also popular in the United Kingdom. For example, The Guardian's recommended style guide has this (emphasis mine):
1am, 6.30pm, etc; 10 o’clock last night but 10pm yesterday; half past two, a quarter to three, 10 to 11, etc; 2hr 5min 6sec, etc; for 24-hour clock, 00.47, 23.59; noon, midnight (not 12 noon, 12 midnight or 12am, 12pm).
A quick look at this list of time notations by language reveals that the following are officially using a dot as the separator:
Since the dot serves the same purpose as a colon, the time is meant to be 7 hours after noon (midday), plus 45 minutes.
Some cultures do not commonly use the 24-hour clock and a number higher than 12 in a time might be unusual. The 24-hour clock is the most common system in the world today and counts the number of hours passed since midnight, from 0 to 23. It is also called "military time" in the United States.
Therefore, "19" means "19 hours after midnight".
The redundant mention of "hours" after the numbers seems to be common in military settings. This answer on the pronunciation of time in 24-hour notation says that it is ingrained in the mind of soldiers. The Art of Manliness, an American website, also says this:
[As for] whether you should say “hours” after giving the time, that somewhat varies by what branch of the military you’re dealing with. If Soldiers and Airmen are saying 2:00pm, they’re a little more likely to give it to you as “fourteen hundred hours,” while Marines or Coast Guardsman [sic] are a little more likely to render it [as] just “fourteen hundred.” Across the branches though, it’s typical to drop the “hours” bit when you’re talking face-to-face and your meaning is obvious, only adding it in conversation and written communication that’s more formal and where you want to make sure the message is clear.
It would appear that the author wanted to add some military slang since the story happened at an airbase.
The phrase "at approximately 19.45" seems unusual for some people who would rather see "about", "roughly" or "around". However, "approximately" reinforces the formality of the sentence, as it is something you might find in reports, legal settings or scientific documents. It sounds much more technical than "around" and again fits with a military setting.
Time and date notations are notoriously difficult to get right. The sum of all the culture-specific quirks (also including number formatting, sorting, case conversions, etc.) is called a locale in computer science. There are as many locales as there are countries and languages. In fact, the "same" language in different countries might have different notations.
For example, in Canada, English and French are the two official languages and have different date notations (dd/mm/yy and yyyy-mm-dd respectively). Canadian English and British English also have different time notations (12-hour clock and 24-hour clock respectively).
In addition to official notations, there are also popular notations that are either:
- historical, because the standard was officially changed in a particular region of the world by its government; or
- a result of outside influences, because another country close by is using a different notation.
In this case, the dot is not the official notation in either Ireland or the United Kingdom. It is, however, a popular notation in the UK.