The speed of light in a vacuum stands at “exactly 299,792,458 metres per second“. The reason today we can put an exact figure on it is because the speed of light in a vacuum is a universal constant that has been measured with lasers; and when an experiment involves lasers, it’s hard to argue with the results. As to why it comes out somewhat conspicuously as a whole number, this is no coincidence- the length of metre is defined using this constant: “the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.”
Prior to a few hundred years ago, it was generally agreed or at least assumed that the speed of light was infinite.
The first known person to question the whole “speed of light is infinite” thing was the 5th century BC philosopher Empedocles. Less than a century later, Aristotle would disagree with Empedocles and the argument continued for more than 2,000 years after.
One of the first prominent individuals to actually come up with a tangible experiment to test whether light had a speed was Dutch Scientist, Isaac Beeckman in 1629. Despite living in a time before lasers- which gives me the chills just thinking about- Beeckman understood that, lacking lasers, the basis of any good scientific experiment should always involve explosions of some kind; thus, his experiment involved detonating gunpowder.
Beeckman placed mirrors at various distances from the explosion and asked observers whether they could see any difference in when the flash of light reflected from each mirror reached their eyes. As you can probably guess, the experiment was “inconclusive”.
