you should ask yourself this question
I thought the REAL answer was "do I feel lucky?" (snicker, snicker....good ol' Clint Eastwood knew how to handle grammar)
Trailing prepositions were good enough for Shakespeare, and they're good enough for me.
I still avoid this one....and I'm even (GASP!) now correcting MY kids...just like mom corrected me and my sibs growing up.
I was thinking of teasing you, even though I know "up" isn't really a preposition there, but naah...
I try to avoid dangling prepositions in some situations, but I find that many word-order inversions sound unduly pretentious ["Of what number were you thinking" may be grammatically preferable to "What number were you thinking of", but sounds unduly stuffy]. I guess, with apologies to Winston Churchill, you'll just have to ask your self up with how much of such awkwardness and stuffiness you are willing to put to satisfy the 18th century grammarians.
Actually, I personally would argue that in English a preposition's proximity to a verb is far more important than its proximity to its object. Many verbs in the English language have special idiomatic meanings when used with certain prepositions; isolating the verb from the preposition tends to dilute such meaning.
In some cases this can be a good thing. Consider the following two questions: