Please advise us the serial no. for us to fill out / fill in the form and return to you.
Fill in.![]()
(not a professional teacher) This is one of those choices that mark the differences between variants of English. In NZ English, either one would be perfectly acceptable, but my instinctive response was "fill out". It's little more than an educated guess, but I'd say that "fill out" would have a 60/40 lead over "fill in" in NZ English.
Is "fill out the blanks" unacceptable?