6.4 Using and Formatting Numbers Appropriately

Every academic or scientific author who must include many numbers while reporting his or her research is faced with the challenge of using and formatting those numbers in an accurate, consistent and appropriate manner. Your department and/or discipline may very well have specific conventions and guidelines regarding the use of numbers that must be observed, and these may be quite specific, or you may have been provided with no guidelines at all for using numbers in a scholarly manner. Unfortunately, there is considerable inconsistency in the advice style guides offer regarding numbers, and even the way in which numbers are referred to while talking about their formatting can be contentious, with some guidance insisting that numbers as numerals rather than words should be called ‘figures,’ while others use ‘numerals’ instead (in this book I use ‘numerals’ to avoid confusion with ‘figures,’ which I use when referring to graphs, illustrations and the like). Style guides tend to assign a number of the variant practices associated with numbers to the conventions of either British or American English, and in some cases the link to one style or the other is clear, but there seems little consensus on some of these matters, and different style guides based in one country can vary in their advice as much as guides claiming to present the two different forms of English. Fortunately, there are also several patterns of usage that are maintained across guidelines, and a healthy share of common sense in using these as you aim for accuracy, consistency and clear communication across all parts of your thesis that include numbers will produce an effective result.

6.4.1 Words or Numerals?

One of the main concerns when using numbers in scholarly writing is whether they should be expressed as words or numerals. In most cases, a threshold value is set: below this value, words are used to express numbers, whereas above it, numerals are used. Unfortunately, there is no single threshold value that applies to every discipline and every thesis, and for very practical reasons. In the humanities and other nontechnical contexts, for instance, the value is often set at 100, whereas in more technical or scientific contexts where numbers tend to be used more extensively, the value is usually 10; for books on music, the value is often 12, and for online writing, numerals are used much more frequently than words, so all numbers may appear as numerals. In addition, such threshold values are only general rules and there are exceptions that apply regardless of the precise value used, as the following points make clear:

  • Large round numbers are usually expressed as words (‘four hundred’ and ‘three million’) or as a combination of words (or abbreviations) and numerals (‘3 million’ or ‘3m.’) even if they are over the threshold value, although this is rarer in the sciences.
  • Approximations as opposed to exact numbers are generally written as words even if they are over the threshold value: ‘I saw about fifty of them.’
  • For a series of quantities, numerals are usually used regardless of whether the numbers are above or below the set value: ‘4, 6, 8, 28, 42, 53, 79, 98, 109 and 127.’
  • When a sentence or, in some cases, a paragraph contains one or more numbers that are over the threshold value as well as numbers that are under it, it is best for both consistency and legibility to use numerals for all the numbers: ‘from 83 to 137’ instead of ‘from eighty-three to 137,’ and ‘between 6 and 13’ instead of ‘between six and 13.’
  • If two sets or categories of numbers are used together in a sentence, clarity and legibility are often improved by using words for one set or category and numerals for the other: ‘the Oxford manuscript consists of forty-four folios with 31 lines on each page, the Worcester manuscript of forty-one folios with 34 lines to a page and the York manuscript of only thirty-nine folios with 36 lines on each page.’
  • All numbers that appear at the beginning of a sentence should be written out as words: ‘Fourteen is the age of consent,’ not ‘14 is the age of consent.’ Alternatively, the sentence can be rephrased or rearranged to avoid placing the number at the beginning (The age of consent is 14), and if the number opening a sentence would be particularly cumbersome when spelled out (e.g., ‘412,724’), this should definitely be done.
  • Numbers used for certain purposes tend to be expressed as numerals regardless of whether they are over the threshold value or not, including page numbers, section and chapter numbers, volume numbers of books and journals, issue numbers of journals, numbers of items in a list, Bible chapter and verse numbers (Genesis 2:4), appendix, table and figure numbers, numbers within tables and figures, numbers in an abstract (though this is not always the case by any means), act and scene numbers, line and column numbers, reference and cross-reference numbers, legal document numbers, numbers that are exact measures, numbers that appear before abbreviations (17 cm), numbers indicating percentages (‘50%,’ but if not exact they occasionally appear as words with ‘per cent’ or ‘percent,’ never with %), numbers recording the scores of tests and games, the numbers of points in scales (a 5-point scale), house, hotel, apartment and building numbers, road and highway numbers, numbers indicating years (‘1960,’ ‘2014’ etc., although they can be written out if necessary – at the beginning of a sentence, for instance) and days of the month, and union and lodge numbers.
  • When a number is part of an already hyphenated compound, a numeral should be used to avoid excessive hyphenation: ‘a 35-year-old man,’ not ‘a thirty-five-year-old man.’
  • While fractions, like whole numbers, can be written as either words or numerals, when whole numbers and fractions are combined, it is better to use numerals: ‘she walked 5¾ miles,’ not ‘she walked five and three-quarters miles.’

Ordinal numbers generally follow the same pattern as cardinal numbers, appearing as words when they are below the threshold value (‘second,’ ‘fifth,’ ‘eighth’ etc.) and as numerals with the appropriate suffix when they are above it (‘74th,’ ‘82nd’ and ‘143rd’). However, some styles will recommend that ordinal numbers be written out in situations where cardinal numbers would not be, or that they be written out on all occasions except in notes, references and quotations (in the last, the format used in the source should be observed). When compound numbers are written as words, they are hyphenated (‘thirty-two,’ ‘eighty-seventh’ etc.) and the same is true of fractions (‘one-quarter’ and ‘two-thirds’), although fractions are often left open and sometimes this is done to indicate a focus on the number or individual parts of a quantity (he gave one third of his inheritance to his sister and another third to his brother) rather than on the proportion or single quantity (he gave two-thirds of his inheritance away). When written out as words, numbers are pluralised in the same way as other words (‘eights and nines,’ ‘seventies’ etc.), although ‘dozen,’ ‘hundred,’ ‘thousand,’ ‘million,’ ‘billion’ and ‘trillion’ tend to remain singular (‘two thousand,’ ‘seven million’ etc.) unless they express indefinite quantities (‘dozens of rabbits’ and ‘thousands of black flies’). Numbers above one can take plural or singular verbs depending on the precise meaning: ‘there were only fourteen participants,’ but ‘fourteen participants is a small sample,’ though the latter could also be worded to reflect both the plural and the singular nature of the concept (fourteen participants result in a small sample).

6.4.2 Arabic Numerals

When numbers are expressed as Arabic numerals, the plurals are formed simply by adding an ‘s’ – no apostrophe is needed (‘1970s’ and ‘low temperatures in the 20s,’ not ‘1970’s’ and ‘low temperatures in the 20’s’); only if the numbers are discussed as entities in themselves might apostrophes be appropriate for clarity (we chose 8’s and 10’s). When numerals appear with abbreviated measures (‘94 mm,’ ‘7 kg’ and ‘30 °C’) there should usually be a space between the numeral and the abbreviation, and the abbreviation should not be pluralised (see Sections 6.3.5 and 6.3.6). When numerals appear with other letters, however, there is generally no space between the numerals and the letters: ‘pp.47ff’ and ‘Item 7a.’ In nontechnical writing, numerals of four (5,698) or five (89,703) digits generally contain a comma after the third digit counting from the right, but in some instances the comma is not used in four-digit numerals (5698); if this is the case, the comma should nonetheless be used in four-digit numerals that appear in any figures or tables (and especially in any columns of tables) that also contain numerals with five or more digits so that alignment is preserved. Often in technical and scientific writing, the commas are not used, but spaces are used instead (‘5 698’ and ‘89 703’), though the four-digit numeral can appear without the space; if so and four-digit numerals appear in figures or tables (again, especially in the columns of tables) along with numerals of five digits or more, the space will need to be added to preserve alignment (for more information on tables and figures, see Section 4.4.1).

The same principle applies to digits after the decimal point: after three digits counted from the left, a space is often used (‘1.479 6’ and ‘7.798 99’), but not always if there are only four digits after the decimal point (1.4796), and alignment should be preserved in tables and figures by adding the space to such four-digit numerals if numerals of five or more digits also appear. In some styles and/or disciplines, the number of digits that appear after the decimal point should be consistent across all numerals used in a particular context or table: if four digits is the maximum number of post-decimal digits in any numeral, all numerals should bear four digits after the decimal, and zeroes can be added to achieve this when necessary. This is by no means a uniform practice, however, so you may only want to apply it in your thesis if it is required by the guidelines you are following or conventional in your discipline. Finally, the decimal point, not the European decimal comma, is used in Arabic numerals in scholarly English prose (‘4.75’ for ‘four point seven five,’ not ‘4,75’). Generally speaking, decimal fractions should feature a zero before the decimal (0.683), especially if they are discussed in relation to quantities of 1.00 and more; if, however, the quantity never reaches 1.00 (as in probabilities and correlation coefficients), the initial zero can be omitted, and the same is the case in ballistics (a .22-calibre rifle).

Technical writing in a number of the sciences can present other formatting challenges and issues which I do not have time or space to cover here, but detailed advice can be found in a number of places. Chapter 13 of Butcher’s Copy-Editing (Butcher et al., 2006) deals with ‘Science and Mathematics Books,’ for instance, and features several sections focussing on numbers (Section 13.1.4 on equations, Section 13.2.5 on miscellaneous items and Section 13.3 on units), as well as separate discussions of astronomy, biology, chemistry, computing, geology and medicine; the chapter also includes an excellent list of references (pp.347–349) for further help while working in these disciplines. Chapter 14 of New Hart’s Rules (Ritter, 2005) focuses on ‘Science, Mathematics, and Computing’ with Section 14.1.3, for example, covering numerals and Section 14.1.4 dealing with units, while other sections provide advice on degrees, temperatures and so on; here, too, there are separate discussions of certain disciplines, including biology, medicine, chemistry, computing, mathematics and astronomy with helpful discussions of the complex formats and punctuation of numerals in these disciplines. Punctuation in the form of commas or spaces is not required at all, however, for numerals used for certain purposes, such as page, column and line numbers, house and hotel room numbers, and reference and library call or shelf numbers. The numerals used for years and eras generally do not feature punctuation either, except BP (Before Present) and long BC dates (for more information on the formats of dates, see Section 6.4.4).

Why PhD Success?

To Graduate Successfully

This article is part of a book called "PhD Success" which focuses on the writing process of a phd thesis, with its aim being to provide sound practices and principles for reporting and formatting in text the methods, results and discussion of even the most innovative and unique research in ways that are clear, correct, professional and persuasive.

The assumption of the book is that the doctoral candidate reading it is both eager to write and more than capable of doing so, but nonetheless requires information and guidance on exactly what he or she should be writing and how best to approach the task. The basic components of a doctoral thesis are outlined and described, as are the elements of complete and accurate scholarly references, and detailed descriptions of writing practices are clarified through the use of numerous examples.

The basic components of a doctoral thesis are outlined and described, as are the elements of complete and accurate scholarly references, and detailed descriptions of writing practices are clarified through the use of numerous examples. PhD Success provides guidance for students familiar with English and the procedures of English universities, but it also acknowledges that many theses in the English language are now written by candidates whose first language is not English, so it carefully explains the scholarly styles, conventions and standards expected of a successful doctoral thesis in the English language.

Individual chapters of this book address reflective and critical writing early in the thesis process; working successfully with thesis supervisors and benefiting from commentary and criticism; drafting and revising effective thesis chapters and developing an academic or scientific argument; writing and formatting a thesis in clear and correct scholarly English; citing, quoting and documenting sources thoroughly and accurately; and preparing for and excelling in thesis meetings and examinations. 

Completing a doctoral thesis successfully requires long and penetrating thought, intellectual rigour and creativity, original research and sound methods (whether established or innovative), precision in recording detail and a wide-ranging thoroughness, as much perseverance and mental toughness as insight and brilliance, and, no matter how many helpful writing guides are consulted, a great deal of hard work over a significant period of time. Writing a thesis can be an enjoyable as well as a challenging experience, however, and even if it is not always so, the personal and professional rewards of achieving such an enormous goal are considerable, as all doctoral candidates no doubt realise, and will last a great deal longer than any problems that may be encountered during the process.

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