Q. I would like to ask if there is a rule in CMOS for writing the numbers on a telephone keypad. For example, when writing the following: “To speak with a specialist, press 3. To cancel your contract, press 4.” Should the numbers be spelled out or kept as figures?
A. Use digits, as you’ve done in your question. The relevant advice is in CMOS 7.81, 7.82, and 8.156, which cover how to style the names of apps, devices, keys, menu items, file formats, and the like. The numbers on a phone qualify as keys on a device or an app, even if the phone predates modern computing.
Most phones, now and in the past, have used numerals for the numbers on their dials or keypads (physical or virtual), as on this rotary dial from Western Electric (ca. 1960, National Museum of American History):
Numerals were also the natural choice as part of telephone exchange names, as in BUtterfield 8, the title of a 1960 movie (based on a novel of the same name by John O’Hara) featuring an Academy Award–winning performance by Elizabeth Taylor. Note the all-caps BU and numeral 8, which together add up to 288 (because B = 2 and U = 8 on a telephone dial/keypad), an exchange for Manhattan’s Upper East Side.
For more on telephone numbers, see CMOS 9.59.