Hello, Paul, and welcome to the Grammar Exchange!
It's obvious to me, from an intuitive standpoint as a native speaker, that the plural is needed, even though the distance is less than one mile: "The sign was 0.05 miles from the house."
I had hoped to be able to substantiate that with reference to a revered grammatical work; however, after spending an hour going through about 20 grammar books, I haven't found anything.
I am done searching for now. It is not a satisfying way to spend an unpaid evening, especially since the answer is already obvious to me, and Wikipedia even confirms it:
I have most of the grammar references listed in the bibliography of that article and didn't find the topic covered in them. Maybe if I spent 6 hours more on the project I'd find a better reference for you.
I'd like to add two points in closing. First, we would use the singular in "The sign was five hundredths of a mile from the house." Second, if you abbreviate ("0.05 mi."), you can avoid the problem.
It is an interesting topic! It might be called a grammatical paradox. ♣