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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.
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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'."
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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.