# Guidelines and Rules for Presenting Numbers in Research Papers

Updated: May 7, 2020

Since numbers are at the heart of research, you should know common rules regarding presenting numbers representing quantitative data in research papers. Knowing these rules will be helpful for writing the material and method section as well as other sections of the paper. If you are aiming to publish in a scientific or scholarly journal, you should check the Guidelines for Authors page of the journal you are targeting for the specific style guide that they follow. Since there are some variations found in different style guides, this will be important to know which guide they adopt. If they do not give this sort of information, it can be helpful to follow some common guidelines prescribed from respected sources like the Council of Scientific Editors. For more detailed coverage of presenting numbers, statistics and mathematical equations in research papers check out: Scientific Style and Format: The CSE Manual for Authors, Editors, and Publishers, The Chicago Manual of Style, and How to Report Statistics in Medicine. My apologies for instances where certain math characters were lost in copying below, specifically those related to exponents and superscript in scientific notation.

1. In scientific and technical texts, with a focus on quantitative data, represent a number with its numeral form, not word form:

*5 samples*

*312 base pairs*

*0.65 mm*

*14 mice*

2. Use the numeral form when comparing with numbers:

*A total of* **5 out of 24 **of the respondents dropped out of the study.

*NOT: **A total of **five out of twenty four **of the respondents dropped out of the study.*

3. Do not begin a sentence with a digit; instead use the word form for the number in question, even if it is above eleven:

*Fifty-six **rats were used.*

*NOT: **56 rats were used.*

Or rewrite the sentence instead of beginning with a lengthy word:

**A total of 4,589 **moths were collected.

*NOT:* **Four thousand five hundred eighty-nine **moths were collected.

4. Separate every three digits with a comma, except with numbers after a decimal. Use a period as a decimal point, and not a comma:

*3.5 %*

*NOT: **3,5 %*

*3,000 participants completed the survey.*

*NOT:**3.000 participants completed the survey.*

5. Be careful with compound nouns that report numbers. All words preceding the head noun must be singular since they function like adjectives. In English, adjectives are always singular:

*A 36-day-old rat.*

*NOT: **a 36 days old rat.*

6. The terms *twice* vs. *two times* have essentially the same meaning, except that *twice*might be favored for being shorter.

*The specimens were disrupted by sonication* **two times **for 45 s at 5°C.

*The specimens were disrupted by sonication* **twice **for 45 s at 5°C.

7. The term ** circa** is used with historical dates, but not typically with measurements. Likewise, the symbol, “” means approximately. Only use it in math applications, not in prose. Instead, use the word “approximately” in running text:

*The temple was destroyed circa*

*1432 BCE.*

*Approximately 542 birds were sighted.*

*NOT: Circa**542 birds were sighted.*

*Approximately 2ml was added to the buffer.*

*NOT: Circa**2ml was added to the buffer.*

*The temperature was approximately* 35C

*NOT:**The temperature was* “” 35

8. Avoid imprecise expressions such as *a 3-fold rise, 2-fold increase, two times as much*, but instead use a more precise numerical percentage or decimal point when reporting precise quantities. This form can be used in a context where an approximation is acceptable, yet the number form should be used, not the word form:

3-fold increase
** NOT: **threefold increase

9. When describing a decade use this form:

*In the 1970s*

*During the 1980s*

*NOT: **In the* *70’s*

*NOT: **In the* *Seventies*

*NOT: I**n the* *70s*

10. Ordinals are commonly used in English to focus on rank, order or a sequence of certain quantitative data. They can be represented in numerical form or word form; for example, *1st, 2nd, 3rd, 4th, first, second third,* and*fourth.* Do not confuse their form:

*23rd*

*NOT:**23th*

*22nd*

*NOT:**22st*

*Eleventh, twelfth, thirteenth,…*

*NOT:**eleventeen, twelveteen,…*

As the CSE points out, “Ordinal numbers generally convey rank order, not quantity. Rather than being expressly enumerative (answering the question “How many?”), ordinals often describe “which”, “what”, or “in what sequence”. Because this function of ordinals is more prose-oriented than quantitative, distinctiveness within the text is less important for ordinal numbers, and undisrupted reading flow and comprehension take precedence”. Hence use the word form for ordinal numbers under 10:

*The* **second **wave toppled the wall.

*The* **third **sample contained only sediment.

*The* **ninth **patient quit the study due to family issues.

Use the numeric form for larger numbers above 10 as the word forms can be lengthy and awkward:

*The 15th attempt was successful.*

*The 25th test was incomplete.*

*We focused on the 19th century.*

*The* **97th **test run

*NOT:**The* *ninety-seventh **test run*

*The* **21st Century**

*NOT:**twenty-first Century*

The numeric form can be used for numbers under 10 if they referred to repeatedly:

*We surveyed 8 subjects: the 1st was most coherent, the 3rd, 4th, and 6th were contradictory, while the 5th, 7th, and 8th were moderately coherent; yet t he 1st could not recall the incident, and the 6th and 8th provided highly specific details of certain events.*

Do not use an ordinal when writing the complete date:

*February 7, 2014.*

** NOT: **February 7th, 2014.

Use the short numerical form rather than the longer word form when discussing centuries:

*Then 19thCentury*

*NOT: **The nineteenth Century*

11. Use the percent symbol (%) whenever a numeral accompanies it. Also, use no space between the number and the percent symbol:

*0. 053%*

*NOT:**0.053 percent*

*NOT: **0.053 %*

12. When two numbers are adjacent, for the sake of readability, spell out one and leave the other as a numerical form:

*As shown in* **Table 2, three **were not recovered.

**NOT: **As shown in**Table 2, 3 **were not recovered.

13. In running text in general, fractions should be represented in word form, rather than numerals. All two-word fractions should be hyphenated, whether as a noun or adjective form.

*Roughly* **one-tenth **of the study subjects reported adverse effects.

*Two-thirds **of this species is found in Brazil.*

*Nearly* * three-quarters of the respondents were pleased with the outcome*.

Yet, for fraction quantities greater than one, use mixed fractions when you do not intend to give a precise value:

*The study site was approximately* **3¾**kilometers from the river.

*The study ran for about* **2½**years.

When a more precise value is desired, use a percentage or decimal form of the number.For mixed numbers with built up fractions, place the whole number close to the fraction, but for solid fractions, place a space between the whole number and the fraction:

** Built up fraction: **9

*Solid fractions: **9 2/3*

14. With numbers that are less than 1.0, use an initial zero to the left of the decimal point:

*0.345*
**NOT:**.345

*P = 0.05*

**NOT:***P = .05*

15. When reporting quantities, consider what unit of measurement and decimal place is most meaningful to report. Round numbers to the most relevant and meaningful digit. For example, while reporting the average length of a group of fish, reporting centimeters would be the most meaningful unit to report. For example, it would be meaningful to report an average length of fish as 12 cm, and it might even be meaningful to report the tenths of Cen termers as in 12.4 cm, yet it would not be necessary to report in hundreds 12.37 cm or thousands of centimeters as in 12.372 cm. Reporting too many decimal points can be distracting to the reader and have little scientific importance. For example, note how it is easy to grasp the general pattern of weight gain in the following two sentences:

*We noticed an average weight gain of 14.4529 g for college students, 12.39815 g for retired couples and 2.99277 g for single parents.*

*We noticed an average weight gain of 14 g for college students, 12 g for retired couples and* *3g for single parents.*

16. When reporting percentages, if the sample you are considering is less than 100, then round to whole numbers. With samples larger than 100, it could be meaningful to report one decimal point. Yet, consider how it will improve the readability and importance of the number. Note this pattern in the sentences below:

*Of the 23 students studied, 32% (7 students) reacted favorably, 49% (11 students) had a neutral* *response, and 19% (4 students) had an adverse reaction to the practice.*

*NOT:**Of the 23 students studied, 32.432% (7 students) reacted favorably, 48.983% (11 students)* *had a neutral response, and 18.594% (4 students) had an adverse reaction to the practice.*

17. In research papers, numbers typically combine with units of measure or symbols, as specified and defined by the International System of Units (Système International d’Unités). These symbols can be alphabetical ( e.g., kg, μg, K, mol, A, s, Hz, mm, mL, min, g, cm) or non-alphabetical (e.g., $, %, S, £, °, ¹). As a general rule, numerals should always accompany these symbols:

*A* **25.0 mL **aliquot of**0.25 M HCNO***(weak acid) is titrated with* **0.15 M NaOH.**

*Near lead smelters and battery plants, air levels typically ranged from* **0.3 to 4.0****μg/m3**

18. Separate symbols from numbers with a single space: