Numbers in Context: Cardinals, Ordinals, and Nominals in American English

1. Introduction

Imagine you are in a restaurant and your server brings over your bill. The bill, like the one shown in Fig. 1, will almost always include three types of number: cardinals, ordinals, and nominals (Nieder, 2005; Wiese, 2004). Cardinal numbers on the bill count sets (e.g., two portions of white rice, seven total items) and quantify elements of conventional scales (e.g., the prices of each item, such as £1.00 for a cup of Kurdish tea), answering the questions “how many?” or “how much?”. Ordinal numbers on the bill, such as the date (e.g., “05/06/2023”) and time (e.g., “18:55:09”), index a position in an ordered sequence (e.g., months in a year, minutes in an hour). In comparison with cardinals, ordinals do not involve quantification. Lastly, nominal numbers on the bill, such as the restaurant's telephone number (e.g., “01509767667”) and postcode (e.g., “LE11 3DU”), act as unique identifiers, “like proper names” (Wiese, 2004, p. 11). The only necessary property of these nominals is that they are unique in a given context, so their selection does not have to involve either quantification or ordering.¹

Several studies have explored the frequency with which morphologically unmarked numbers (e.g., “one” and “30,” but not “first” and “30th”) are used (Coupland, 2011; Dehaene & Mehler, 1992; Dorogovtsev, Mendes, & Oliveira, 2005; Jansen & Pollmann, 2001; Woodin, Winter, Littlemore, Perlman, & Grieve, 2024), showing, for example, that people use smaller numbers more frequently than larger ones and round numbers more frequently than unround ones. These studies tend to assume, either explicitly or implicitly, that cardinal numbers are the most prototypical number type (Wiese, 2004, p. 2), and thus that the analyzed numbers reflect mostly quantitative uses (see discussion in Cummins, 2015, Ch. 6). This assumption is problematic when aggregated number frequencies are cited to make claims about, for example, the linear or logarithmic scaling of numerical cognition (Dehaene & Mehler, 1992) or the imprecision of the approximate number system (Woodin et al., 2024; see also Rinaldi & Marelli, 2020). These claims are predicated on quantitative uses of numbers, so the extent to which they are warranted depends on to what extent the number frequency data capture quantitative, cardinal uses. The research literature also contains untested claims about non‐cardinal numbers, some of which conflict. For example, Nieder (2005, p. 178) describes nominals as “atypical,” whereas Wiese (2004, p. 11) makes the claim that “nominal assignments are actually quite common in our daily lives.” Both statements relate to the frequency with which nominals are used, relative to cardinals and ordinals, but no study has assessed which type of number, if any, is more or less common in contemporary, industrialized cultures. Information about the relative frequencies of number types is relevant to studies that have investigated the order in which these number types are acquired by children (e.g., Colomé & Noël, 2012; Fischer & Beckey, 1990; Miller, Major, Shu, & Zhang, 2000) because input frequency could explain why certain number types are acquired earlier or later than others.

This paper is the first to conduct a corpus analysis of number types, exploring the relative proportions of cardinal, ordinal, and nominal numbers in a corpus of American English. In doing so, we establish a necessary initial baseline for analyses of number frequencies whose hypotheses implicitly relate to cardinal uses of numbers, particularly those based on large‐scale natural language data. Overall, this paper provides a first snapshot into how numbers are used in context, shedding new light on numerical communication, as well as numerical and mathematical cognition.

2. Background

Several studies have investigated frequencies for morphologically unmarked numbers in corpora. Dehaene and Mehler (1992) looked at single number words (i.e., no multiword phrases, e.g., “one hundred and twenty one”) from 0 to a billion in an American English corpus of more than 1 million words (Francis & Kučera, 1982). They found that number frequency decreases with magnitude in a logarithmic fashion, citing this trend to support the idea that numerical cognition itself is logarithmically scaled. They also found that the round numbers 10, 20, 50, and 100 are used frequently, relative to their magnitude. Other studies have reported similar patterns regarding magnitude and roundness for numbers 2–1,000 in approximation contexts (preceded by “about”) in a 40 million word corpus of articles from the English newspaper The Times from 1994 (Jansen & Pollmann, 2001); numbers 1–20 in the 100 million word British National Corpus (BNC Consortium, 2007) and numerals and English number words 1–100 on the Internet (both: Coupland, 2011); the frequencies of web pages containing numerals (Dorogovtsev et al., 2005); and numbers 0 to a billion in the British National Corpus (Woodin et al., 2024). However, none of these studies distinguished between cardinal, ordinal, and nominal numbers.

There is no easy way of differentiating between different uses of numbers without investigating each number closely in its communicative context. Dehaene and Mehler (1992) examined number words such as English “second” and “nineteenth,” whose morphology suggests that they are ordinal. However, many English ordinals are not morphologically marked, such as when people talk about their “top 5 songs.” Thus, the same number, sometimes without morphological adjustment, can have an ordinal reading when embedded in a construction such as “top N” or “bottom N,” but a cardinal reading when embedded in a construction such as “5 people.” Even morphologically marked words like “fifth” and “eighth” that may usually be ordinal can have a cardinal meaning in some contexts, as in fractions (e.g., “an eighth of a cup of butter”). Other English constructions cue a nominal interpretation, like when a number is preceded by the word “number” itself, as in “bus line number 23” and “player number 23” (Wiese, 2004, pp. 270–274). However, it is also possible to cue a nominal reading without the word “number,” as in “bus line 23” and “player 23,” and there are nominal uses of numbers that do not follow this pattern at all, such as “call 911.” Therefore, the task of identifying different number types is more complicated than simply identifying numbers with certain morphologies or in pre‐defined constructions, requiring a careful reading of the contexts in which these numbers are used.

Using corpus methods to identify number types and report their relative frequencies is important for the study of many topics relevant to numerical and mathematical cognition. One of these topics is children's acquisition of number concepts. While most research in this area has explored the acquisition of cardinal numbers, some studies have compared the relative order with which ordinal and cardinal numbers are acquired by child speakers of Belgian French (Colomé & Noël, 2012), U.S. English (Fischer & Beckey, 1990), and U.S. English and Mandarin Chinese (Miller et al., 2000), finding that cardinal uses of numbers are acquired before ordinals. There are no data on the acquisition of nominals relative to cardinals and ordinals, but it is presumed that they are acquired later (see discussion in Wiese, 2004). However, studies that look at the acquisition of different number types by children would be informed by the relative uses in adults in their respective languages, if we take adult language to be the target of acquisition. For example, nominals may be acquired later because they are less frequent in the language input children receive, rather than this late acquisition having anything to do with nominals being more cognitively difficult. Thus, corpus analyses of the relative frequency of cardinals, ordinals, and nominals would establish baselines that could inform developmental research in mathematical cognition.

Such corpus analyses of number types are also relevant to debates about whether people think about numbers linearly or logarithmically (e.g., Dehaene, 2003; Moeller, Pixner, Kauffman, & Nuerk, 2009; Piantadosi, 2016). As well as behavioral research, language data are often cited as a source of evidence in these debates: Dehaene and Mehler (1992) argue that the higher relative frequency of smaller numbers in corpora of English and other languages (e.g., Dutch, Japanese, Kannada) supports a logarithmic model. However, claims about the scaling of numerical cognition concern quantification, and so are predicated on cardinality, when cardinal, ordinal, and nominal numbers are conflated in the data cited to corroborate these claims. Thus, it is possible that number type is a confounding factor in these analyses, as the relationship between frequency and magnitude is likely to differ between number types. For example, ordinals and nominals may tend to be smaller than cardinals because, among other reasons, reports of ordinal rank usually mention the very best or worst cases of a category (e.g., “top 10 university”), and nominal player numbering usually starts at 1, and sports teams usually do not have hundreds or thousands of players. In comparison, quantitative uses of numbers can assume far higher values, such as money (e.g., “a billion dollars”). If ordinals and nominals do skew smaller than cardinals, they would drive up frequencies of smaller numbers in corpus studies investigating morphologically unmarked numbers, potentially presenting an issue when arguments about the logarithmic scaling of the mental number line are predicated on these studies.

Relative frequencies of number types are also relevant for new methods of studying the approximate number system in distributional semantics, a computational approach that represents meanings as word vectors based on the contexts in which words are used. For example, even when “doctor” and “physician” do not appear in the same texts, they tend to appear in the same kinds of text (Günther, Rinaldi, & Marelli, 2019), providing a cue to their meaning, following Firth's (1957, p. 179) famous credo that “you shall know a word by the company it keeps.” Using distributional semantics, Rinaldi and Marelli (2020) demonstrated they could derive several properties associated with the approximate number system from text data alone for English and other languages (e.g., German, Russian, Chinese). Taking vector variance as a proxy, they showed that larger numbers are used less precisely than smaller numbers, just as the approximate number system is argued to be increasingly imprecise for larger quantities (DeWind, Adams, Platt, & Brannon, 2015; Shepard, Kilpatric, & Cunningham, 1975). However, these results are predicated on word vectors derived from all contexts in which morphologically unmarked numbers are used, while the approximate number system is only relevant to quantitative, cardinal contexts. Just as is the case with the other studies mentioned above, it is possible that Rinaldi and Marelli's (2020) results are affected by the distribution of cardinals, ordinals, and nominals changing as a function of magnitude. For instance, if small numbers are relatively more likely to be ordinal or nominal (as suggested above), vector variance may increase for larger numbers because larger numbers are more likely to be cardinal, and cardinals may be used less precisely in general. If true, Rinaldi and Marelli's (2020) word vectors would not necessarily reflect the approximate number system.

Consistent with the idea that numerical communication is less precise for larger numbers, Woodin et al. (2024) showed that at higher magnitudes, users of British English tend to use more round (morphologically unmarked) numbers, defined as multiples of 10 and sometimes 5 in the decimal system typically used in English (e.g., Dorogovtsev et al., 2005; Sigurd, 1988). Round numbers are often (but not always) used imprecisely (e.g., Jansen & Pollmann, 2001; Krifka, 2009; Sigurd, 1988), such as when rounding 248 up to 250 when counting attendees at a conference. However, Woodin et al. (2024) also did not differentiate quantitative, cardinal uses of numbers from nominal and ordinal uses, and it is unclear to what extent roundness governs the use of nominals and ordinals, given that quantification is the prototypical context for rounding (e.g., “around 100 cars,” “nearly 20 meters high”). Roundness is probably irrelevant to nominals, as rounding nominals alters their referent: for example, rounding Cristiano Ronaldo's player number 7 to 10 would denote another player entirely. In comparison, one study showed that French speakers do round ordinals in time‐telling contexts, such as rounding 3:08 to 3:10 (Van der Henst, Carles, & Sperber, 2002; see also Gibbs & Bryant, 2008), and United Kingdom university reports often structure “top N” lists around multiples of 5, as in “Warwick repeats top 10 success” (Cummins & Franke, 2021, p. 12). Furthermore, when interpreting ranked lists, people more favorably interpret rank improvements that cross round number boundaries (e.g., rank 11 to rank 10) than those that do not (e.g., rank 10 to rank 9) (Isaac & Schindler, 2014). Therefore, roundness may influence the frequency with which round and unround ordinals are used to some extent, although it is unclear whether this factor is as relevant to ordinals as it is to cardinals.

Relating the use of round numbers to the approximate number system is further complicated by the idea that the kinds of number considered appropriate for use in approximation contexts in English may differ between subtypes of cardinal number: “pure” cardinal numbers that count sets (people, plants, buildings, etc.) and measurements that quantify elements of conventional scales (cost, length, duration, etc.). Particularly, approximate use of measurements, unlike pure cardinals, may not exclusively involve round numbers: Cummins (2015, Ch. 6) argues that whereas the English expression “about 19 people” is infelicitous, “about 19 minutes” is felicitous, because it implies that “19 minutes” has been rounded to the nearest minute (e.g., from 18 minutes 47 seconds). This difference derives from measurement scales being recursively divisible into subscales, like seconds within minutes, milliseconds within seconds, and so on. Rounding measurements in English may therefore involve rounding subscales to the nearest scale unit, rather than necessarily to multiples of 5 and 10. Consequently, the trend for multiples of 5 and 10 to be used more frequently at higher magnitudes in English may be stronger for pure cardinals, as measurements may rely less on multiples of 5 and 10 for approximation. If so, another approach that does not investigate imprecision exclusively through the use of conventionally “round” numbers may be required to obtain an accurate picture of approximation across magnitude.

The use of cardinal, ordinal, and nominal numbers may also differ across registers: varieties of the same language that differ in terms of their communicative context or goal (Trudgill, 1983, p. 101). A major distinction here is based on whether a register is spoken or written: Biber (2012) cites a range of research showing that language use varies drastically between speech and writing in English, particularly academic writing (e.g., Biber & Gray, 2010; Conrad & Biber, 2009; Kennedy, 1998). Other work has found differences between more specific registers, for example, between manuals, letters, and novels in English and German (Neumann, 2014), and narration and speech within English novels (Egbert & Mahlberg, 2020). Regarding numerical language, Woodin et al. (2024) found that registers in British English speech and writing, respectively, such as non‐fiction writing and oral presentations, contained more decimals and larger numbers, and more unique numbers, than less informational registers. As discussed above, however, this study did not distinguish between cardinals, ordinals, or nominals. Other studies have exclusively investigated cardinal numbers, finding that English news texts are quantitatively dense (e.g., Cushion, Lewis, & Callaghan, 2017; Maier, 2002). It is possible that news texts use numbers for their purported ability to boost perceived objectivity (Barchas‐Lichtenstein et al., 2022; Porter, 1995) and credibility (Koetsenruijter, 2011). Exploring the distribution of number types across registers (e.g., academic writing, fiction writing) can tell us what types of numerical information (e.g., quantitative, non‐quantitative) are relevant in different communicative contexts with different goals.

In writing, different number types may be represented in different representational formats—numerals (e.g., “122”) and number words (e.g., “one hundred and twenty‐two”; see Chrisomalis, 2020, Ch. 6). Whether a number is written as a numeral or as a number word is often prescribed by style guides (e.g., The Chicago Manual of Style, 2017b). For example, nominal phone numbers and zip codes, as well as ordinal years and page numbers, are probably almost always represented as numerals in English; presumably, nobody would write the U.S. zip code 95340 as “nine five three four zero,” for example. In contrast, cardinals do not prescribe representational format as strongly; for instance, both “30 people” and “thirty people” are felicitous. Within cardinals, it is also possible that measurements are more likely to be written as numerals than pure cardinals for reasons of concision: in English, units of measurement are generally allowed to be abbreviated, or represented as a symbol when paired with numerals (e.g., “12 mm,” “$100”) but not number words (e.g., “twelve millimeters,” “one hundred dollars”). In cases where representational format is more flexible (e.g., for cardinals), there may be greater pressure to keep unround numbers short by representing them as numerals, given that unround number word expressions are typically longer than round ones (e.g., “two hundred and one” vs. “two hundred”). Moreover, certain representational formats may be preferred for certain number types: for example, mixtures of numerals and multiplier words (e.g., “$13 trillion,” “2.5 billion”) are exclusively selected for cardinal meanings in English. Therefore, representational format itself can serve as a cue that helps readers to infer how numbers are used—a probabilistic cue, rather than the more categorical cue provided by constructions (e.g., “bus line number 23,” “player number 23”; Wiese, 2004, pp. 270–274) and morphology (e.g., “sixth,” “10th”).

In this paper, we present the first corpus analysis investigating the different types of numbers used in modern, industrialized societies: cardinals (pure cardinals, measurements), ordinals, and nominals. We focus on morphologically unmarked numbers (e.g., “3” and “20,” not “3rd” and “twentieth”), as these are the types of numbers typically aggregated in analyses of number frequencies that are often cited to make claims about cognition. These numbers also seem to be more ambiguous when divorced from context than morphologically marked numbers, which are likely to be predominantly ordinal, with, as mentioned above, the exception of their use in fractions. We conduct this analysis by manually annotating a sample of concordances from the Corpus of Contemporary American English (COCA; Davies, 2008). Concordances, or concordance lines, are lines of text that show how words (in our case, numbers) are used in context. With these concordances, we investigate the relative frequencies of the number types overall and in relation to factors such as magnitude, roundness, register, and, in writing, representational format, in addition to the interaction between these factors. In doing so, we delve deep into the connection between numerical communication and important aspects of numerical cognition and mathematical cognition.

3. Methodology

All data, analysis scripts, and detailed information about the methodology described in this section can be found in the following OSF repository: https://osf.io/mdtb4/.

4. Results

This section begins with an overview of how many concordances are cardinal (either pure cardinal or measurement), ordinal, nominal, or otherwise, and the main functions of these numbers (Section 4.1). We then report the frequency of each number type across registers (Section 4.2) and magnitudes (Section 4.3), and the extent to which number types of different magnitudes are round or unround (Section 4.4). Finally, in writing (fiction, newspapers, magazines, academic), we report the extent to which the different number types are written as number words and numerals, and whether this representational format depends on roundness (Section 4.5).

5. Discussion

This study is the first corpus analysis investigating how often morphologically unmarked numbers are used as cardinals, ordinals, or nominals. Our results show that, in American English, cardinals—both pure cardinals and measurements—are dominant, followed by ordinals, then nominals. Cardinals dominate all orders of magnitude except 1,000–10,000, in which there is a high number of ordinal years, such as 1977 and 2024. Only for cardinals do round numbers (i.e., multiples of 5) dominate overall and increase with magnitude. Among quantitative uses of numbers, measurements are more common than pure cardinals, often quantifying money. In comparison with other registers, academic writing contains a lower proportion of measurements, as well as a higher proportion of ordinals and, to some extent, nominals. In writing, pure cardinals and measurements are usually represented as number words, but measurements—especially larger, unround ones—are more likely to be numerals. Ordinals and nominals are mostly written as numerals.

The relative frequencies of cardinals, ordinals, and nominals we report establish a baseline for analyses of aggregated number frequencies, whose hypotheses regarding numerical cognition hinge on quantitative, cardinal uses of numbers (Coupland, 2011; Dehaene & Mehler, 1992; Dorogovtsev et al., 2005; Jansen & Pollmann, 2001; Woodin et al., 2024), at least those analyses focused on English. Our findings generally confirm the assumptions of these previous analyses, showing that cardinals are the most prototypical number type (Wiese, 2004, p. 2) when it comes to morphologically unmarked numbers (i.e., not “twelfth,” “20th,” etc.), comprising 83.4% of concordances. As for nominals, our results support Nieder's (2005, p. 178) assertion that nominals are “atypical,” given that these are indeed the least often occurring number type. Nonetheless, nominals are still relatively “common” (Wiese, 2004, p. 11), comprising a non‐negligible 4.8% of concordances, which increases to 7.3% if we count the 81 concordances whose nominal meaning is based on ordinal (e.g., house numbers) or cardinal (e.g., “the S&P 500”) information. Ordinals are more frequent than nominals, comprising 11.8% of concordances. Therefore, we recommend that researchers at least acknowledge ordinals and nominals when aggregating number frequencies, even when cardinals are the focal point of the analyses.

In a separate procedure in addition to our main analysis reported above, we also identified 1,259,237 numbers whose morphology suggests they are ordinal (e.g., “tenth,” “13th”). These morphologically marked numbers represent 13.4% of the total combined unmarked and marked numbers. With this information, we can estimate the percentages of cardinals, ordinals, and nominals across all numbers in COCA (i.e., not just the morphologically unmarked ones, on which our main analysis is concentrated). We use the percentage of cardinals, ordinals, and nominals from our sample to estimate counts for all numbers in COCA. We then add to the ordinal count the 1,259,237 marked numbers, which we assume are ordinal, and estimate the percentages again. When we do this, 72.2% (N = 6,798,882) of all numbers are cardinal, whereas 23.6% (N = 2,225,437) are ordinal, and 4.6% (N = 393,031) are nominal.⁵ These statistics show that, compared to the main analysis, the proportion of ordinals increases, and the proportion of cardinals decreases. However, cardinals are still clearly dominant.

The fact that cardinals dominate our sample suggests that the finding that smaller numbers are used more often than larger numbers, cited in support of a logarithmic representation of numbers (Dehaene & Mehler, 1992), may be expected to hold even if number frequencies were based exclusively on cardinals. This argument is corroborated by the fact that ordinals and nominals, which are less frequent than cardinals, do not skew strongly toward lower magnitudes in our data, and so are unlikely to drive the bias toward smaller numbers by themselves. Another finding that may be expected to replicate in a cardinals‐only sample is that larger numbers are used more approximately than smaller numbers (Rinaldi & Marelli, 2020; Woodin et al., 2024), which may reflect the increasing imprecision of the approximate number system at higher magnitudes (DeWind et al., 2015; Shepard et al., 1975). Indeed, our data demonstrate directly that frequencies of round numbers (i.e., multiples of 5), which are often used approximately (e.g., Krifka, 2009; Solt, Cummins, & Palmović, 2017), increase with magnitude only for pure cardinals and measurements. This is true despite measurements possibly relying less on multiples of 5 for approximations (see Cummins, 2015, Ch. 6). Generally, most of the pure cardinals and measurements in our dataset are round, whereas most of the ordinals and nominals are unround. Of course, this result does not mean people never round ordinals or nominals—there is evidence for roundness being relevant to ordinal numbers (Cummins & Franke, 2021; Isaac & Schindler, 2014; Van der Henst et al., 2002)—but our dataset indicates that rounding is much more common for quantitative uses of numbers, which are more closely tied to the approximate number system.

Regarding approximation, Winter and Marghetis (2023) note that the lexical differentiation of English reveals a strong communicative need to express quantity approximately. English has many lexical items to express approximate quantity, including quantifiers (e.g., “a few,” “several,” “more than,” “most”), range expressions (e.g., “10–15”), nouns (e.g., “a bulk of,” “a heap of”), and number modifiers (e.g., “N‐ish”). Our data suggest that even with the lexical items that afford the most precision—numbers—we so often use them approximately, as round numbers. This is particularly the case for very high numerical magnitudes. In fact, even some ostensibly unround numbers at higher magnitudes are intended as approximations, as a form of numerical hyperbole (see Kao, Wu, Bergen, & Goodman, 2014; Lavric, 2010), such as the use of a large round number plus one, as in “a million and one ideas.” Although these hyperbolic numbers are unround, they are based on round numbers, which act as a benchmark (Dehaene, 1997, Ch. 4; Gunasti, 2016), with an added “one” to indicate that the quantity is even larger than an already large amount. Constraining the interpretation of these numbers as imprecise is the fact that they are often unrealistically high in context (e.g., “thousand and one gas lamps”), or quantify things that are difficult to count precisely (e.g., “ideas,” “tadpoles”), at least at the high magnitudes discussed.

People talk and write most often about the things that are most communicatively relevant to them: language users in colder climates discuss ice and snow more frequently (Regier, Carstensen, & Kemp, 2016); English speakers in vision‐based Western cultures use vision‐related words more frequently (Winter, Perlman, & Majid, 2018), and addition‐based language is used more frequently than subtraction‐based language (Winter, Fischer, Scheepers, & Myachykov, 2023), mirroring an addition bias found in behavioral studies (Adams, Converse, Hales, & Klotz, 2021). Our analysis of functions shows that, in COCA, pure cardinals most often count people, while measurements most often quantify money, ordinals most often represent years, and nominals are most frequent in communications numbers and website programming code. Speakers of American English may assign numbers to people, money, and time more often as it is culturally important to quantify these concepts, as when keeping records of population figures, event attendees, financial transactions, stock market values, historical events, text publication dates, and so on.

While previous studies explored large‐scale register differences in number use in English without differentiating between number types (Woodin et al., 2024), or by only looking at cardinal numbers (e.g., Cushion et al., 2017; Maier, 2002), we investigated register differences in the use of number types. The results for speech, fiction, magazines, and newspapers align with the overall results: measurements are the most frequent, followed by pure cardinals, ordinals, and then nominals. In contrast, academic writing contains more ordinals (e.g., years in citations) and nominals (e.g., zip codes in author addresses). This result is broadly consistent with other register studies that found academic writing contains especially distinctive language (e.g., Biber & Gray, 2010; Conrad & Biber, 2009; Kennedy, 1998). This register difference highlights the importance of conducting research on a representative sample across a range of registers if the results are intended to generalize beyond one's sample to, for example, a language variety (e.g., American English) more broadly.

Certain aspects of our findings cannot be expected to generalize beyond modern American English. For a start, nominal numbers may be much less relevant or even absent from non‐industrialized cultures that do not have phone numbers, credit cards, and so on. Regarding ordinals, even if it were true that many cultures often use numbers to represent years, the specific numbers used for this function would depend on the calendrical system used. In our sample, the ordinals in the range 1,000–10,000 are only frequent due to the Gregorian calendar used in the United States beginning 2024 years ago at the time of writing. In comparison, the Republic of China calendar used in Taiwan begins in the Gregorian year 1912, meaning that the Gregorian year 2024 is ROC era 113 (Wilkinson, 2000). As we have discussed (see Section 3.1), there are some issues with COCA's sampling of texts that may limit its generalizability even to other kinds of contemporary American English, like casual conversation. Our results may also be time‐dependent, with, for example, representational formats of numbers known to vary across time (e.g., Berg & Neubauer, 2014; Chrisomalis, 2020; MacQueen, 2010).

In COCA's written subcorpora, different number types are typically represented in different formats (see Chrisomalis, 2020, Ch. 6). Representational format seems strongly prescribed for ordinals and nominals: the overwhelming majority of these numbers are numerals. In comparison, whereas cardinals are more often written as number words in general, representational format is far more varied for this number type, especially for measurements. The increased formatting of measurements as numerals compared to pure cardinals may be because, conventionally in English, units of measurements are permitted to be abbreviated or represented as a symbol when used with numerals (e.g., “100 m”, “$20”) but not number words (e.g., “one hundred meters”, “twenty dollars”). Due to this convention, there may be a greater communicative pressure for writers to use numerals to keep measurements short. Communicative pressure toward concision may also help explain why larger, unround measurements are especially likely to be written as numerals: unround number word expressions increase in length with magnitude (e.g., “one thousand and fifty three” is longer than “one thousand”) as they are formed partly through the concatenation of round number words, while round number word expressions do not necessarily become longer with magnitude (e.g., “one million” is shorter than “one thousand”). Hence, writing unround measurements as numerals yields a greater improvement in concision than for round measurements, especially for larger numbers. Of course, authors do not have total freedom in their written representation of numbers; rather, they can be constrained by the prescriptions of writing style guides. Indeed, regarding round numbers, the Chicago Manual of Style's (2017a) online FAQ section states, “The whole numbers one through one hundred followed by hundred, thousand, or hundred thousand are usually spelled out,” whereas numerals are prescribed elsewhere. Even so, style guide prescriptions like this often reflect non‐arbitrary concerns of economy, such as avoiding expressions that are overly long.

Given that, as discussed in the introduction, any morphologically unmarked number could in principle be cardinal, ordinal, or nominal, how does a language user know how to interpret a number? As well as cues provided by constructions, like “bus line number 23,” “player number 23” (Wiese, 2004, pp. 270–274), “top N,” and “bottom N,” our results reveal other probabilistic cues on which language users may rely. Owing to the predominance of cardinals in our dataset, English speakers may expect most numbers to be cardinal, with measurements being slightly more probable than pure cardinals. This expectation may be strengthened if the number is a round number word (e.g., “thousand”), while the predicted probability of the number being ordinal or nominal may increase if it is an unround numeral (e.g., “162”). Collocations may provide an additional clue: if the number is succeeded by a noun (e.g., “people,” “letters”), for example, English speakers may assign a higher probability to the number being cardinal. Another factor, unexplored in this paper, is punctuation: for example, four‐digit numbers with commas (e.g., “2,024”) are very likely to be cardinal, while the same number without commas (e.g., “2024”) is more likely to be interpreted as a year. These factors and more may interact in forming predictions about number use.

The frequency information we present is relevant for developmental research on children's acquisition of number concepts (e.g., Colomé & Noël, 2012; Fischer & Beckey, 1990; Miller et al., 2000). Specifically, we showed how dominant the use of different number types is in adult American English, which provides the input for acquisition of English by children in the United States. Hence, our work raises the possibility that the order in which children acquire cardinals, ordinals, and nominals may be affected by differential exposure to these number uses, rather than acquisition order being associated solely with cognitive difficulty. Our data also provide insight into the contexts in which these number types appear, with pedagogical applications. For example, while explicit instruction on differences between number types may not be common in language teaching, it may be helpful to introduce cardinal, ordinal, and nominal numbers in the contexts in which these numbers are usually found, with corpus‐driven examples that are actually attested in language—such as “5,000 to 8,000 people” and “thirty seven million Americans” for cardinals—rather than artificially constructed sentences. Teaching numbers in their most common contexts first should have more immediate applicability in everyday conversations. This idea is consistent with more general calls from corpus linguists for the most common concepts, established through corpora, to be prioritized in language teaching (e.g., Hunston, 2002; Kaya, Uzun, & Cangır, 2022; Sinclair & Renouf, 1988; see McEnery & Xiao, 2011 for a review).

Overall, this paper shows how numbers are actually used in context in a corpus of American English, uncovering a picture of numerical communication more complex and nuanced than aggregated number frequencies reveal by themselves. These results have important insights for numerical and mathematical cognition, with language serving as a channel through which the approximate number system can be observed and analyzed.

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