Numbers

A. Write ordinal ranges as they would be pronounced; in other words, repeat the ordinal ending in all cases (1st–2nd, 24th–25th, 101st–200th). Another way to look at this is that the ordinal ending is an integral part of an ordinal number and shouldn’t be omitted except in special cases.

One special case is for dates. Days of the month are typically written as cardinals in Chicago (and US) style, though they’re usually pronounced as ordinals: May 9 (pronounced May 9th). A range of days would also be written without ordinal endings: May 5–9. But when a day is used alone or ahead of the month, it’s normally expressed as an ordinal: the 9th of May or, in a range, the 5th–9th of May (where both ordinal endings are required). See also CMOS 9.33.

Note that when you spell out an ordinal, you should write through or to instead of using an en dash: first through tenth (not first–tenth). See also CMOS 6.83 (for en dashes) and 9.6 (for ordinals).

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

A. In the abbreviated range 176–77, there’s little chance that a reader might think you’re referring to pages 176 and 77. But in 176r–77v, the intervening r makes it more likely that “77v” could be mistaken for a reference to the verso of page 77. So our editors decided to repeat the hundreds place for clarity. We’ll consider adding this exception to our rules for abbreviating inclusive numbers—along with any others that might be warranted—in a future edition of CMOS.

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

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):

Rotary dial from a Western Electric telephone circa 1960 with holes around the perimeter showing numbers 1 through 9 corresponding to eight three-letter groups ABC through WXY (starting at 2) plus zero for the operator

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.

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

A. Amounts of less than one can usually be treated as singular when expressed as simple fractions—as in your three examples—but plural when expressed as decimal fractions. The difference is related to how such expressions would be spelled out or read aloud:

1/4 mile = one-fourth of a mile or a quarter of a mile or a quarter mile (among other variations)

7/8 mile = seven-eighths of a mile

2/3 cup = two-thirds of a cup

A decimal fraction, by contrast, would normally be read as a plural:

0.25 miles = (zero) point two five miles (rather than twenty-five hundredths of a mile)

But note that an abbreviated unit of measure is usually the same for both singular and plural quantities. So you’d write “0.25 mi.” even though “mi.” would be read as “miles.” See also CMOS 9.21 and 10.73.

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

A. You have nothing to fear: Though commas are omitted from years that include no more than four digits, they’re recommended for years that run to five digits or more. So about eight thousand years from now (or just under 7,975 years as of April 2025)—when the year 9999 will have turned into 10,000 (as in 10,000 CE, or AD 10,000 if you prefer)—you can start adding commas to years to help you keep track of all those digits.

We don’t know why commas are omitted from four-digit years. But check back with us once commas are required again for everyday use. Maybe by then CMOS will have grown to more than 10,000 pages. If so—and assuming it’s still published in print and fits in a single volume (or two or more consecutively paginated volumes)—you should be able to turn to page 10000 or later to find out whether we’re still omitting commas from five-digit page numbers.

For more on years (including abbreviations like AD and CE), start with CMOS 9.36; for page numbers, see 9.63. For spelling out numbers versus using digits, start with 9.1.

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

A. That’s a challenging question! Let’s start with a few numbers and how we would suggest spelling them out—on both sides of the decimal point:

1,357,201.5: one million, three hundred fifty-seven thousand, two hundred one and five tenths

1,357,201.58: one million, three hundred fifty-seven thousand, two hundred one and fifty-eight hundredths

1,357,201.580: one million, three hundred fifty-seven thousand, two hundred one and five hundred eighty thousandths

1,357,201.5803: one million, three hundred fifty-seven thousand, two hundred one and five thousand eight hundred three ten-thousandths

Note that we’ve used commas between groups of numbers to the left of the decimal point but not to the right, which reflects how the numbers are grouped (and punctuated) as digits. But we’ve treated the numbers to the left of the decimal point as a single value rather than as a series (which might require a serial comma before and).

The rules for hyphenation are the same on both sides of the decimal point (see CMOS 7.96, section 1, “numbers, spelled out”). But note that Chicago’s preference for hyphenating simple fractions doesn’t apply to five tenths in the first example above, which simply names the number in the tenths place. It does, however, apply to an ordinal fraction like ten-thousandths:

five-tenths (a simple fraction)

five tenths (the number in the tenths place; see first example above)

ten-thousandths (the ten-thousandths place; see last example above)

See also CMOS 7.96, section 1, “fractions, simple.” Finally, note that some writers add and when spelling out certain numbers that include hundred (three hundred and fifty-seven thousand; two hundred and one); Chicago omits this and (see CMOS 9.5).

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

A. You’re right: We can’t really know what day 12:00 a.m. refers to. So unless it’s clear from context, it’s best to specify both, as in 12:00 a.m., April 12–13—or, better yet, midnight, April 12–13. Because even though 12:00 a.m. is usually understood to mean midnight and 12:00 p.m. noon, both of those expressions are potentially ambiguous, at least outside of calendar apps and the like (see CMOS 9.40).

The twenty-four-hour system has a slight advantage here, but you still need two separate numbers. In that system, midnight on April 12 would be expressed as 2400 hours, whereas the beginning of April 13 would be 0000 hours. Those times are identical, but the numbers used to express them—and the dates they refer to—are different. See also CMOS 9.41.

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

A. You’ve punctuated your hypothetical telephone numbers—which are in the form most often used in the United States and Canada—in order of most familiar, most straightforward, and least conventional.

Putting the area code in parentheses is supposed to suggest that dialing it is optional. As area codes have increasingly become necessary even for local calls, this convention has nonetheless remained common.

As for accessibility, in our brief tests (using numerals rather than x’s), all three formats were read as phone numbers by both Microsoft Word’s Read Aloud feature and Microsoft’s Narrator—that is, as a series of ten individual digits with a pause after the third and sixth and not as three large numbers, two of them in the hundreds and one of them in the thousands. And each was automatically turned into a callable phone number link in various messaging and email apps on a smartphone.

But only the first two are mentioned in the recommendations published by the International Telecommunication Union, so we’d advise using one of those (the ones without periods). See also CMOS 9.57.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]

A. You’re right that a single-character Unicode fraction like ½ (U+00BD, vulgar fraction one half) won’t match a fraction like 1/72 that relies on the forward slash (or solidus) character. One approach that can work in HTML (which is what you’re viewing right now) is to use a fraction slash (U+2044) instead of an ordinary forward slash (U+002F, the character that shares a key with the question mark on English-language QWERTY keyboards).

Unlike the forward slash, the fraction slash is designed to kern tightly to any character immediately before or after it. Best of all, the numbers before and after the slash will automatically go into fraction mode, adjusting their size and position relative to the slash (though not in all fonts):

Fraction slash, no superscripts or subscripts:
1⁄2 and 2⁄3 and 3⁄4 and 5⁄8 and 3⁄16 and 1⁄72

Forward slash (solidus), with superscripts and subscripts:
¹/₂ and ²/₃ and ³/₄ and ⁵/₈ and ³/₁₆ and ¹/₇₂

Both versions have a certain consistency to them, but the first set of fractions is better at matching the look of Unicode’s vulgar fractions. And according to the applicable Unicode chart (in what Unicode defines in its Help pages as an “informative note”), the fraction slash is intended “for composing arbitrary fractions”—which is the goal in this case.

But this approach won’t automatically work across applications. In a book manuscript composed in Word, you should probably use ordinary numbers with the forward slash—as in “1/72”—and ask your publisher or typesetter to format the fractions for you (e.g., using the available tools in a program like InDesign), specifying that you want them all to look like Unicode’s ½.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]

A. Use numerals for 150,000. The applicable principles are as follows:

• Spell out numbers one through one hundred (Chicago’s general rule).
• Spell out multiples of one through one hundred used in combination with hundred, thousand, or hundred thousand.

So you would spell out “five thousand” and “one hundred thousand” but use digits for 150,000—because 150 would normally be rendered as a numeral.

But if you’re following Chicago’s alternative rule of using digits for 10 and up, all such larger numbers are usually given as numerals. Rather than, for example, “fifteen thousand” or “15 thousand,” you’d write 15,000.

For more details, see CMOS 9.2, 9.3, and 9.4. For numbers with million, billion, and so forth, see CMOS 9.8.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]