23 Numbers
23.1.3 Percentages and Decimal Fractions
23.1.7 Addresses and Thoroughfares
23.1.8 Parts of Published Works
23.2.3 Other Punctuation within Numbers
23.3.2 Decades, Centuries, and Eras
23.4 Numbers Used outside the Text
This chapter offers general guidelines for presenting numbers. These guidelines are appropriate for most humanities and social science disciplines, but disciplines that rely heavily on numerical data may have more specific guidelines. If you are writing a paper in the natural or physical sciences, mathematics, or any other very technical field, follow the conventions of the discipline. For style guides in various disciplines, see the bibliography. For advice on numbering the pages and parts of your paper, see the appendix.
If you are writing a thesis or a dissertation, your department or university may have specific requirements for presenting numbers, which are usually available from the office of theses and dissertations. If you are writing a class paper, your instructor may also ask you to follow certain principles for presenting numbers. Review these requirements before you prepare your paper. They take precedence over the guidelines suggested here.
23.1 Words or Numerals?
The most common question in presenting numbers is whether to spell them out in words (twenty-two) or give them in numerals (22). When the number is followed by a unit of measure, you must also decide whether to give that unit in words (percent) or as a symbol (%) or an abbreviation.
The guidelines presented in 23.1–23.3 pertain to numbers used in the text of your paper. For numbers used in tables, figures, and citations, see 23.4.
Unless otherwise specified, numerals here means arabic numerals (1, 2, 3, etc.). For roman numerals (i, ii, iii, etc.), see table 23.1.
23.1.1 General Rule
Before you draft your paper, you should decide on a general rule for presenting numbers and follow it consistently. Which rule you choose depends on how often you use numerical data and the conventions of your discipline. For situations in which you might modify this rule, see 23.1.2–23.1.8.
In the humanities and social sciences, if you use numerical data only occasionally, spell out numbers from one through one hundred. If the number has two words, use a hyphen (fifty-five). Also spell out round numbers followed by hundred, thousand, hundred thousand, million, and so on (but see 23.1.2.3). For all other numbers, use arabic numerals. Follow this pattern for numbers that are part of physical quantities (distances, lengths, temperatures, and so on), and do not use abbreviations for the units in such quantities (see 24.5).
Table 23.1. Roman numerals
After seven years of war came sixty-four years of peace.
The population of the three states was approximately twelve million.
He catalogued more than 527 works of art.
Within fifteen minutes the temperature dropped twenty degrees.
If your topic relies heavily on numerical data, follow a different rule: spell out only single-digit numbers and use numerals for all others.
This study of 14 electoral districts over seven years included 142 participants.
He hit the wall at 65 miles per hour, leaving skid marks for nine feet.
In the sciences, your general rule may be to use numerals for all numbers, except when they begin a sentence (see 23.1.2.1). You may also use abbreviations for quantities (see 24.5).
The mean weight proved to be 7 g, which was far less than predicted.
With any of these rules, use the same principles for ordinal numbers (first, second, etc.) that you use for standard ones. Add st, nd, rd, or th as appropriate.
On the 122nd and 123rd days of his trip, he received his eighteenth and nineteenth letters from home.
23.1.2 Special Cases
In a few common situations, the general rule discussed in 23.1.1 requires modification.
23.1.2.1 NUMBERS BEGINNING A SENTENCE. Never begin a sentence with a numeral. Either spell out the number or recast the sentence, especially when there are other numerals of a similar type in the sentence.
Two hundred fifty soldiers in the unit escaped injury; 175 sustained minor injuries.
or, better,
Of the soldiers in the unit, 250 escaped injury and 175 sustained minor injuries.
When spelling out numbers over one hundred, omit the word and within the term (not two hundred and fifty).
23.1.2.2 RELATED NUMBERS. Ignore the general rule when you have a series of related numbers in the same sentence that are above and below the threshold, especially when those numbers are being compared. In these examples, all are expressed in numerals.
Of the group surveyed, 78 students had studied French and 142 had studied Spanish for three years or more.
We analyzed 62 cases; of these, 59 had occurred in adults and 3 in children.
If you are discussing two sets of items in close proximity, ignore the general rule and, for clarity, spell out all numbers in one set and use numerals for all numbers in the other.
Within the program, 9 children showed some improvement after six months and 37 showed significant improvement after eighteen months.
23.1.2.3 ROUND NUMBERS. Spell out a round number (a whole number followed by hundred, thousand, hundred thousand, million, and so on) in isolation (see 23.1.1), but give several round numbers close together in numerals. You may also express large round numbers in a combination of numerals and words. (See also 23.1.4.)
Approximately fifteen hundred scholars attended the conference.
but
They sold 1,500 copies in the first year and 8,000 in the second.
These changes will affect about 7.8 million people in New York alone.
23.1.3 Percentages and Decimal Fractions
Use numerals to express percentages and decimal fractions, except at the beginning of a sentence (see 23.1.2.1). Spell out the word percent, except when you use many percentage figures and in the sciences, where the symbol % is usually preferred (with no intervening space after the number). Notice that the noun percentage should not be used with a number.
Scores for students who skipped summer school improved only 9 percent. The percentage of students who failed was about 2.4 times the usual rate.
Within this system, the subject scored 3.8, or 95%.
but not
The average rose 9 percentage points.
When you use fractional and whole numbers for the same type of item in the same sentence or paragraph, give both as numerals.
The average number of children born to college graduates dropped from 2.4 to 2.
Put a zero in front of a decimal fraction of less than 1.00 if the quantity expressed is capable of exceeding 1.00. When decimal quantities must be 1.00 or less, as in probabilities, correlation coefficients, and the like, omit the zero before the decimal point.
a mean of 0.73
a loss of 0.08
p < .05
a .406 batting average
For fractions standing alone, follow the general rule (see 23.1.1) for spelling out the parts. If you spell the parts, include a hyphen between them. Express in numerals a unit composed of a whole number and a fraction. If you use a symbol for the fraction, there is no intervening space between the number and the fraction.
Trade and commodity services accounted for nine-tenths of all international receipts and payments.
One year during the Dust Bowl era, the town received only 15/16 of an inch of rain.
The main carving implement used in this society measured 2½ feet.
23.1.4 Money
23.1.4.1 US CURRENCY. If you refer only occasionally to US currency, follow the general rule (see 23.1.1), and spell out the words dollars and cents. Otherwise use numerals along with the symbol $. Omit the decimal point and following zeros for whole-dollar amounts, unless you refer to fractional amounts as well.
Rarely do they spend more than five dollars a week on recreation.
The report showed $135 collected in fines.
Prices ranged from $0.95 up to $10.00.
Express large round numbers in a combination of numerals and words.
The deficit that year was $420 billion.
23.1.4.2 OTHER CURRENCIES. For currencies other than that of the United States, follow the pattern for the US dollar. Most currencies put unit symbols before numerals. Even though European nations represent decimal points with commas instead of periods, you may use periods, except in direct quotations from sources. In contexts where the symbol $ may refer to non-US currencies, these currencies should be clearly identified.
When she returned, she had barely fifty euros to her name.
The household records show that it cost only £36.50.
Its current estimated worth is ¥377 million.
If you subtract Can$15.69 from US$25.00,…
Most European nations now use the unified currency called the euro (€), but if you are writing about topics from the period before 2002, you may encounter such currencies as the French franc (F), German deutsche mark (DM), and Italian lira (Lit). British currency is still expressed in pounds (£) and pence (p.), though before decimalization in 1971, it was expressed in pounds, shillings, and pence (for example, £12 17s. 6d.). Note that billion in traditional British usage as well as in some other foreign languages means a million million, not a thousand million; to avoid confusion, be sure to accurately represent such distinctions.
In more technical contexts, it may be best to use the three-letter codes for current and historical currencies defined by the International Organization for Standardization in standard ISO 4217, which is available on the organization’s website. Use a space between the code and the amount.
If you subtract EUR 15.69 from USD 25.00,…
23.1.5 Time
For references to times of day in even increments of an hour, half hour, or quarter hour, spell out the times, with a hyphen between parts. If necessary, specify in the morning or in the evening. You may use o’clock, although it is now rare in research writing.
The participants planned to meet every Thursday around ten-thirty in the morning.
When emphasizing exact times, use numerals and, if necessary, a.m. or p.m. (lowercase and roman; see also 24.4.1). Always include zeros after the colon for even hours.
Although scheduled to end at 11:00 a.m., the council meeting ran until 1:37 p.m.
In either situation, use the words noon and midnight (rather than numerals) to express these specific times of day.
For use of words or numerals in dates, see 23.3.
23.1.6 Names with Numbers
Some types of personal, governmental, and organizational names include numbers given in either words or numerals. (See also 22.1.)
■ Leaders. Emperors, sovereigns, or popes with the same first name are differentiated by capitalized roman numerals (see table 23.1).
Charles V
Napoleon III
Elizabeth II
Benedict XVI
■ Family members. Male family members with identical full names are often differentiated with roman or arabic numerals (see also 24.2.1). Note that there are no commas between the name and the numeral, unless the name is inverted, as in a list.
Adlai E. Stevenson III
Michael F. Johnson 2nd
but
Stevenson, Adlai E., III
■ Governments and political divisions. Certain dynasties, governments, governing bodies, political and judicial divisions, and military units are commonly designated by an ordinal number before the noun. Spell out and capitalize numbers through one hundred (with a hyphen between the parts of the number, if relevant); use numerals for those over one hundred.
Nineteenth Dynasty
Fourteenth Congressional District
Fifth Republic
Forty-Seventh Ward
Eighty-First Congress
Tenth Circuit
109th Congress
101st Airborne Division
■ Churches and religious organizations. Spell out and capitalize numbers before the names of churches or religious organizations in ordinal form (with a hyphen between the parts of the number, if relevant).
Twenty-First Church of Christ, Scientist
■ Secular organizations. Express local branches of fraternal lodges and unions in numerals following the name.
American Legion, Department of Illinois, Crispus Attucks Post No. 1268
United Auto Workers Local 890
23.1.7 Addresses and Thoroughfares
Follow the general rule (see 23.1.1) for the names of local numbered streets. State, federal, and interstate highways are always designated with numerals, as are street or building addresses and telephone and fax numbers. Note that in text the elements of a full address are separated by commas, except before a zip code. See 24.3.2 for abbreviations in addresses.
The National Park Service maintains as a museum the house where Lincoln died (516 10th Street NW, Washington, DC 20004; 202-426-6924).
Ludwig Mies van der Rohe designed the apartments at 860–880 North Lake Shore Drive.
Interstate 95 serves as a critical transportation line from Boston to Miami.
23.1.8 Parts of Published Works
With the exception of roman-numeral page numbers (as in the front matter of a book; see 16.1.5, 18.1.5), numbers in parts of published works are given in arabic numerals, regardless of the general rule (see 23.1.1) or their appearance in the work itself. See also 22.3.2.3, 23.2.2.
chapter 14
part 2
act 1, scene 3
page 1024
23.1.9 Equations and Formulas
Numbers in equations and formulas are always given as numerals, regardless of the general rule (see 23.1.1). For detailed guidance on presenting mathematical expressions, see chapter 12 of The Chicago Manual of Style, 16th edition (2010).
23.2 Plurals and Punctuation
23.2.1 Plurals
Form the plurals of spelled-out numbers like the plurals of other nouns (see 20.1).
Half the men surveyed were in their thirties or forties.
Form the plurals of numbers expressed in numerals by adding s alone (not ’s).
The pattern changed in the late 1990s as more taxpayers submitted 1040s online.
To fly 767s, the pilots required special training.
23.2.2 Commas within Numbers
In most numbers of four or more digits, set off thousands, hundreds of thousands, millions, and so on with commas. In the sciences, commas are often omitted from four-digit numbers.
1,500
12,275,500
1,475,525,000
Do not use a comma within a four-digit year; do use one for a year with five or more digits (see also 23.3).
2007
10,000 BC
Do not use a comma in page numbers, street addresses, telephone or fax numbers, zip codes, decimal fractions of less than one, or numbers included in organization names.
page 1012
0.1911 centimeters
15000 Elm Street
Committee of 1000
23.2.3 Other Punctuation within Numbers
Numbers sometimes include other internal punctuation. For periods (decimals), see 23.1.3 and 23.1.4; for colons, see 23.1.5; for hyphens, see 23.1.1 and 23.1.3; for dashes, see 23.2.4.
23.2.4 Inclusive Numbers
To express a range of numbers, such as pages or years, give the first and last (or inclusive) numbers of the sequence. If the numbers are spelled out, express the range with the words from and to; if they are expressed in numerals, use either these words or a connecting hyphen with no space on either side. In some settings, such as citations, always use hyphens (see chapters 16–19). Do not combine words and hyphens in expressing inclusive numbers.
from 45 to 50
but not
from 45–50
45–50
but not
forty-five-fifty
For inclusive numbers of one hundred or greater, you may either use full numbers on either side of a hyphen (245–280 or 1929–1994) or abbreviate the second number. Table 23.2 shows one system of abbreviation.
This system works well for page numbers, which never include commas (see 23.2.2). For numbers that include commas, use the system shown in table 23.2, but repeat all digits if the change extends to the thousands place or beyond. Never abbreviate roman numerals (see table 23.1).
6,000–6,018
12,473–79
128,333–129,114
xxv–xxviii
For years, give all digits for a span that includes more than one century. Also give full dates in a system in which dates are counted backward from a specific point (most notably BC, “before Christ,” and BCE, “before the common era”). Otherwise, use the system shown in table 23.2. see 23.3 for more on date systems.
the years 1933–36
the winter of 1999–2000
15,000–14,000 BCE
115 BC–AD 10
Table 23.2. Abbreviation system for inclusive numbers
23.3 Date Systems
23.3.1 Month, Day, and Year
Spell out the names of months when they occur in text, whether alone or in dates. Express days and years in numerals, and avoid using them at the beginning of a sentence, where they would have to be spelled out (see 23.1.2.1). Do not abbreviate references to the year (“the great flood of ’05”). For abbreviations acceptable in tables, figures, and citations, see 24.4.2.
Every September, we recall the events of 2001.
but not
Two thousand one was a memorable year.
For full references to dates, give the month, the day (followed by a comma), and the year, in accordance with US practices. If you omit the day, omit the comma. Also omit the comma for dates given with seasons instead of months; do not capitalize the names of seasons (see 22.1.2). If material you are quoting uses British-style dates (15 March 2007), do not alter them.
President John F. Kennedy was assassinated on November 22, 1963.
By March 1865, the war was nearly over.
The research was conducted over several weeks in spring 2006.
Note that within complete dates, days are generally not given as ordinals—that is, the numerals are not followed by st, nd, rd, or th. Use these endings only with spelled-out numbers when you specify the day without the month or year.
The date chosen for the raid was the twenty-ninth.
but not
The events occurred on June 11th, 1968.
23.3.2 Decades, Centuries, and Eras
In general, refer to decades using numerals, including the century (see 23.2.1 for plurals). If the century is clear, do not abbreviate numerals (“the ’90s”); instead, spell out the name of the decade. The first two decades of any century do not lend themselves to either style and should be described fully for clarity.
The 1920s brought unheralded financial prosperity.
During the fifties, the Cold War dominated the headlines.
Many of these discoveries were announced during the first decade of the twenty-first century.
Refer to centuries using either numerals or lowercase, spelled-out names (see 23.2.1 for plurals). If the century is spelled out and used as an adjective preceding a noun that it modifies, as in the second example, use a hyphen; otherwise, do not (see 20.3.2).
The Ottoman Empire reached its apex in the 1600s.
She teaches nineteenth-century novels but would rather teach poetry from the twentieth century.
The most common designations for eras use the abbreviations BC (“before Christ”) and AD (anno Domini, “in the year of the Lord”). Some disciplines use different designations, such as BCE and CE (see 24.4.3). AD precedes the year number; the other designations follow it. For inclusive numbers with eras, see 23.2.4.
Solomon’s Temple was destroyed by the Babylonians in 586 BC and again by the Romans in AD 70.
23.4 Numbers Used outside the Text
The preceding sections provide guidelines for presenting numbers in the text of your paper. Numbers used in tables, figures, source citations, and lists are subject to some of their own rules. For additional advice, see the appendix.
23.4.1 Numbers in Tables, Figures, and Citations
In general, use arabic numerals to present numerical data in tables and figures. For a discussion of numbers in tables, including table titles, see 26.2; for numbers in figures, including figure captions, see 26.3.
With few exceptions, arabic numerals are also used to cite volume numbers, edition numbers, and page numbers and other locators. For a discussion of numbers in bibliography-style citations, see 16.1.5 and chapter 17; for numbers in author-date citations, see 18.1.5 and chapter 19.
23.4.2 Enumerations
You may use numerals (and letters) to enumerate points discussed in the text, in appendixes, or in materials related to drafting your paper.
23.4.2.1 LISTS. Your text may contain lists of items that you choose to enumerate for emphasis. When such a list is relatively short, incorporate it into a single sentence. Be sure that all the items are grammatically parallel (all noun phrases, all adjectives, or the like). Each item should be preceded by an arabic numeral in parentheses. If there are more than two items, each should be followed by a comma (or, if the item is complex in structure, a semicolon; see 21.3). If the list is an appositive, use a colon to introduce it; otherwise, do not use punctuation in this position (see 21.4).
Wilson’s secretary gave three reasons for his resignation: (1) advancing age, (2) gradually failing eyesight, and (3) opposition to the war.
The committee strongly endorsed the policies of (1) complete executive power, except as constitutionally limited; (2) strong legislative prerogatives; and (3) limited judicial authority, especially when it interfered with the committee’s own role.
If you are already using arabic numerals in parentheses for other purposes, substitute lowercase letters for the numbers.
Haskin’s latest theory has more than one drawback: (a) it is not based on current evidence and (b) it has a weak theoretical grounding.
If the items in the list are longer or you wish to give them greater emphasis, arrange them in a vertical list. Introduce the list with a complete sentence followed by a colon. Again, be sure that all the items are grammatically parallel, and begin each one with a bullet or an arabic numeral followed by a period, without parentheses. If the items are complete sentences, capitalize the first letter in each item and use terminal periods; otherwise use lowercase letters and no periods (see 21.1). Align the numerals on the periods and any lines that run over with the first word in the first line.
My research therefore suggests the following conclusions:
1. The painting could not have been a genuine Picasso, regardless of the claims of earlier scholars.
2. It is impossible to identify the true artist without further technical analysis.
23.4.2.2 OUTLINES. In some situations, you may include an outline or a similar enumeration in an appendix to your paper, or in a draft stage of the paper (see 6.2.1). Use the following system of notation, consisting of letters and roman and arabic numerals, and indent each level by one further tab (usually a half inch). You should have at least two items to list at each level; if you do not, reconsider the structure of the outline. If the items are phrases, capitalize them sentence style (see 22.3.1) and do not use terminal punctuation. If they are complete sentences, capitalize and punctuate them as you would any other sentence (see 6.2.1 for an example).
I. Wars of the nineteenth century
A. United States
1. Civil War, 1861–65
a) Cause
(1) Slavery
(a) Compromise
i) Missouri Compromise
ii) Compromise of 1850 …
b) Result
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II. Wars of the twentieth century
A. United States
1. First World War …