# Guidelines and Rules for Presenting Numbers in Research Papers

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:

*345 Hz*

*5 mm*

19. Close up the space between a non alphabetical symbol and a number:

*5%*

*$4*

Note, one exception to this rule: The Council of Scientific Editors recommend a space here, while the American Medical Association recommends no space:

CSE Style: *45* *°C*

*AMA Style:* *45°C*

Ultimately, you will need to follow the style guide recommendations from the journal that you planning to submit your research paper to.

21. When representing numbers in a range, use the word “to” between numbers, and not a hyphen or a dash:

*Regional unemployment rates ranged from* **1.2% to 33.3%.**

*NOT:**Regional unemployment rates ranged from* *1.2% - 33.3%.*

When using the preposition “between” to introduce a range, always accompany it with “and”, not a hyphen or a dash:

*In a range* **between 4 and 10cm.**

**NOT: **In a range**between 4 - 10cm.**

When the range includes numbers with several digits, do not leave out the leading numbers of the second number of the range:

*1958 to 1962*

*NOT:**1958 to 62*

*1,724 to 1,736*

*NOT:**1,724 to 36*

You can use a single unit symbol alone after second number in a range of numbers, except for when the symbol is non-alphabetical and must be closed up to the number (e.g., $,%).

*30 to 45 mL*

*120 to 200 Hz*

*10 to 20 min*

*40 to $60*

*NOT:**40 to $60*

*13% to 22%*

*NOT:**13 to 22%*

Be careful when expressing a change in value in a range, especially when using terms like “increased”, “decreased” or “changed”. Use language that clarifies that the change is in the range or in the final amount.

*Growth increased* **by a range of **1.5 g/d to 3.5 g/d.

*Growth increased* **from an initial value **a range of 1.5 g/d**to a final value of **3.5 g/d.

*NOT: **Growth increased* *by **1.5 g/d to 3.5 g/d.*

*NOT: **Growth increased* *from**1.5 g/d to 3.5 g/d.*

22. When reporting dimensions, use a multiplication symbol and not the letter “x” or the word “by”, and leave a space between the multiplication symbol and the numbers:

*22* *18* *16*

*NOT: **22 by 18 by 16*

When the focus is on expressing one range changing to a new range, place a hyphen between numbers to improve readability:

*increased from 25–34 mm to 28–42 mm *

*NOT:** increased from 25 to 34 mm to 28 to 42 mm*

23. For a series of numbers, place the symbol after the last number, except in cases where the symbol must be close to a number:

*14, 15, 18, and 54 Hz*

*$21, $37, and $41*

*10%, 14% and 34%*

24. Express large numbers or very small number in powers of 10, scientific notation.

*3.8 × 104*

*NOT: **38,000*

*7.35 x 108*

*NOT:**735,000,000*

*3.51´10-6*

*NOT:**0.000,003,51*

25. For large numbers that are not expressing high precision, a combination of numbers and words are acceptable:

*The population is around 25 million.*

**NOT: **The population is around 25, 000, 000.

26. With common symbols of math operations ( separate the symbol and number with a space or thin space. Use the math symbol and not the letter x to represent multiplication. Do not use these sybmols in running text:

2 × 7 = 14

*NOT: **27=14*

The averages equaled the total of all samples from plot A plus plot B.

** NOT: **The averages = the total of all samples from plot A + plot B.

When these symbols are used as modifiers of words, then close up the space between them and the term they modify. Also, do not place two or more operator symbols side by side.

*100*

*at*

Also, do not place two or more operator symbols side by side.

The total was greater than

** NOT: **The total was

27. For symbols used in calculus, refer to the Association of American Publishers for extensive details directions on their markup in manuscripts. For details on how to present vectors, scalars, tensors, matrices and determinants, see Scientific Style & Format: The Council of Scientific Editors, Chapter 12.

28. Brackets, parentheses, and braces in mathematics are referred to as enclosures or “fences”. In math, their order of use is parentheses within brackets within braces, and the reverse is order follows in non-mathematical prose: braces within brackets within parentheses.

mathematics: { [ ( ) ] }

prose or non-mathematics: ( [ {} ] )

29. In the following math expressions no space (closed up to the number) is required:

When expressing multiplication without the multiplication symbol:

*2b*

*ac*

Between fences and enclosures and the variables on either side of them:

*(a − 12)x*

*(2p − 6bc)(1 − a)*

*a|y|*

Between terms and their subscripts as in the following terms:

*94*

*cos3*

*cx-2z*

With the symbols plus and minus when used to indicate positive or negative value for numbers:

-5

+18

-12*x*

When expressing a ratio using a colon, close up the space:

1:3

** NOT: **1 : 3

Place a space between all common math operators: +, =, -,

30. Ratios, percentages, and proportions are commonly used to simplify and report research findings. Whenever using them, be sure to report a numerator and denominator of that accompanies them; otherwise it will be difficult to interpret them in a meaningful way. For instance 50% could be 2 of 4 samples had a positive result or 6,000 of 12,000 had a positive result. While both are examples of 50%, they would have a very different meaning in research. Separate the two numbers of a ratio by a colon, with the first typically being the numerator and the second the denominator:

*The ratio of negative results was 3 to1 (946:329).*

**NOT: **The ratio of negative results was 3 to1.

Proportions are the result of dividing the numerator by the denominator, with the numerator typically a subset of the items in the denominator:

The proportion of subjects experiencing adverse effects was 0.032 (21/651).

** NOT:** The proportion of subjects experiencing adverse effects was 0.032 .

To express a proportion as a percentage, multiply it by 100.

*The percentage of subjects experiencing adverse effects 3.2% (21/651).*

*NOT:**The percentage of subjects experiencing adverse effects 3.2% (21/651).*

**Exercise 4**

After studying the points made above about presenting numbers, correct the sentences below with errors related to numbers.

1. 4 assays were performed.

2. Measurements were made for just about one hundred and fifty snakes.

3. Since 80ies’ it has been shown that X plays a role in Y.

4. The 2th and 3th samples were negative.

5. This accounted for most of the total biomass.

6. Many informations can be found in the literature.

7. A lot of water was needed.

8. The deprotonated ion increased by about 2-fold.

9. For this case, the factor was just about 0.90, i.e. very close to one.

10. Three of percent of the samples were positive.

11. Each stock was valued at ten thousands of dollars.

12. Circa 10 mM was used.

13. 17x4=68

14. 9 4

15. The total was

16. The population is around 25, 000, 000.

17. We found 15 % similarity.

18. The range increased from 25 to 34 mm to 28 to 42 mm.

19. As shown in table 3, 2 there was a significant increase.

20. The average cost per sample was 40 to $60

21. As many as 13 to 22% of the participants expreienced no adverse effect.

22. One tenth of the subjects reported improved vision.

23. We detected a difference of 0.000,003,51.

24. Statistical significance was set at .05

25. Rates ranged from 1.2% to 33.3%.

**Check Answers Below:**

**Exercise 4**

Four assays were performed. **Begin a sentence with the word form (four), not a digit (4).**Measurements were **taken** for **approximately 150** snakes.**Since the 1980sit has been shown that X causes Y.**The **2nd**and **3rd**were negative for…**…Accounted for the majority of the biomass.a great deal of informationcan be found in the literature.A great deal of** **water was needed.**Give a precise numerical percentage rather than something vague like “about 2-fold”.Avoid vague and informal term such as “just about” and “very close to”. Instead substitute “approximately” and “nearly”.**Three percent** **of the samples were positive.**Each stock was valued at **ten-thousand dollars** **Approximately10** **mM was used.** **(Use space between common math operators)** *94* (use no space between numeral and exponent)The total was greater than (Avoid presenting two math operator symbols side by side).The population is around 25 million. (Use the word form when giving large imprecise numbers).We found 15% similarity. (No space between numerals and non-alphabetical symbols).The range increased from 25–34 mm to 28–42 mm. (When reporting a change of ranges, use a hyphen between numbers to improve readability).As shown in Table 3, three subjects dropped out. (When two numbers are adjacent, for the sake of readability, spell out one and leave the other as a numerical form).

20. The average cost per sample was $40 to $60 (When presenting a range, both numbers must be accompanied by the non-alphabetical symbol).

21. As many as 13% to 22% of the participants experienced no adverse effect. (When presenting a range, both numbers must be accompanied by the non-alphabetical symbol).

22. One-tenth of the subjects reported improved vision (hyphenate two-word fractions).

23. We detected a difference of *3.51* ´*10-6* (write out very large or very small numbers in scientific notation)

24. Statistical significance was set at 0.05 (Place a zero before a decimal place.

25. Rates ranged from 1.2% to 33.3%. (Use the preposition “to” between numbers in a range, not a hyphen).

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