Numbers

Q. Correct to hyphenate “four-hundredth birthday”? Seems right, but I can’t find a source. Thank you!

A. Though the hyphen doesn’t do any harm in your example, you can normally leave it out. See the hyphenation guide at CMOS 7.96, section 1, under “numbers, spelled out,” which says this (the rule is stated on the right and the examples are on the left):

twenty-eight
three hundred
nineteen forty-five
five hundred fifty-two contestants
twenty-eighth
three hundredth
five hundred fifty-second
contestant

Twenty-one through ninety-nine hyphenated; others open. Applies equally to cardinals and ordinals. See also fractions, simple.

The last example—“five hundred fifty-second contestant” (some writers would add “and” before “fifty-second”)—is analogous to “four hundredth contestant” (or “four hundredth birthday”); “fifty-second” is hyphenated in the example in CMOS because “fifty-two” is normally hyphenated.

Note that some of the numbers above would normally be written with numerals (e.g., 552nd). And though four hundred is usually spelled out according to Chicago’s general rule for numbers (which says to spell out the whole numbers zero through one hundred and extends to multiples of a hundred), you’d usually write 400th if you were following Chicago’s alternative rule (see CMOS 9.29.3, and 9.4).

It should also be noted that a number like four hundred is hyphenated sometimes—for example, when it forms part of a compound modifier (“four-hundred-acre farm”); see section 1 of the hyphenation guide, under “number + noun.”

[This answer relies on the 18th edition of CMOS (2024) unless otherwise noted.]