J.k. rowling's thoughts platform nine and three-quarters
In choosing the number of the concealed platform that would take young witches and wizards to boarding school, I decided that it would have to be a number between those of the Muggle platforms — therefore, it was clearly a fraction. This raised the interesting question of how many other fractional platforms lay between the whole-numbered platforms at King's Cross, and I concluded that were probably quite a few. Although these are never mentioned in the book, I like to think that it is possible to take a version of the Orient Express off to wizard-only villages in continental Europe (try platform seven and a half), and that other platforms may be opened on an as-required-basis, for instance for large, one-off events such as Celestina Warbeck concerts (see your ticket for details).
The number nine and three-quarters presented itself without much conscious thought, and I liked it so much that I took it at once. It is the 'three-quarters' that makes it, of course.