I've just stumbled over an article where somebody stated, that "the number one is not a rate, so is certainly not the rate at which anything (the ﬂow of time included) happens".
Well, I would like to ask this person to wallpaper his flat. He will need a certain amount of squaremeters of wallpaper to do so. If he devides this by the squaremeters of his flat, he will get a dimensionless number (squaremeters per squaremeters =1), which is dependent on a.) the number of walls (each wall will separate the room in two spaces, the next wall can be a either part of it (three rooms) or dividing it into four rooms, and so on...
Of course, it is also depending on b.) the height of the room as well, another nice question.
There will be (a lot of) flats, which have a "rate" of exactly one, i.e. the same amount of squaremeter wallpaper is needed like the ground floor of that flat exhibits, so the value will be an all dimensionless "one"!