As a longtime [former] editor, I developed my own rule of using the singular (in this case, foot) if the number was less than one unit. If the number was greater than one unit, I used the plural (for example, 1.1 feet).

Colleagues of mine aver that I may be right but would like me to produce an actual published/documented rule to that effect.

Can someone quote the CMS or another authoritative source on this matter?

Many thanks.
According to Swan, Practical English Usage:

"With fractions below 1, we normally use of a + singular noun. The same structure is common with decimals below 1. 'three quarters of a ton', '0.1625 cm - nought point one six two five of a centimetre'.

However, decimals below 1 can also be followed directly by a plural noun. 'Nought point one six two five centimetres'.

Fractions and decimals over 1 are normally followed directly by a plural noun. 'one and a half hours', '1.3 milliimeters'."
Students: Are you brave enough to let our tutors analyse your pronunciation?
As is apparent in Mister Micawber's response, using the abbreviation (e.g., ft) avoids the whole issue, if abbreviations are acceptable! Can't avoid it spoken, though.
Mr. Swan doesn't seem to take a strong stance ("normally" followed by "However"). Down here in the U.S. of A., we might say that's 6 of one and half a dozen of another.

Perhaps someone else could weigh in?

Thanks much, Mr. Micawber.