5 Common errors in representing numbers and units of measurement
Numbers and units of measurement occur in almost every sentence in the results sections of engineering and physical sciences research papers, and they are imperative to how the paper is read and understood. Mistakes in representing numbers and units of measurement can leave scope for misinterpretation of your data. This article will help you understand the common mistakes in scientific representation and how you can avoid them. But before we get to that, let’s get a few basics clear.
Numbers are often referred to as “ordinal”, “nominal”, or “cardinal” on the basis of the format or style in which they are written as well as the function they fulfill. Ordinal numbers represent the position or order of appearance (e.g., 2nd, thirtieth, 51st, hundredth); nominal numbers are used as names or references to identify something (e.g., car number “88”, jersey number “20”). Cardinal numbers are often written or spelled out in their numerical form and primarily answer the question of “how many” (e.g., 4, eight, 13, fifty-seven).
Units of measurement are standardized to enable a uniform system of reference and to avoid misunderstandings due to conversion errors. The international system of units (SI units or colloquially called the metric system) is the most widely used system of measurements. Although alternative systems such as the CGS (centimeter, gram, and second) and FPS (foot, pound, and second) systems are still in use, most academic journals insist on the use of SI units.
Physical sciences and engineering papers tend to have certain types of errors in the representation of numbers and units of measurement. In this article, we have listed some of of these errors so that you can be more careful and avoid them in your papers.
1. Errors in representing numbers
Journals and some style guides differ in recommendations for representing numbers. Some prefer that cardinal numbers below ten be spelled out unless they are accompanied by a unit (e.g., nine subjects but 9 cm). A standard practice irrespective of which style is preferred is to spell out numerals that appear at the beginning of a sentence, title, or heading. An alternative revision would be to rephrase the sentence such that the numeral does not appear at the beginning.
Incorrect: 14 locations were chosen for the stress measurements.
Correct: Fourteen locations were chosen for the stress measurements.
Alternative revision: We chose 14 locations for the stress measurements.
One exception to this rule is when the numeral is part of a chemical name. In such cases, the first letter of the syllabic part of the name should be capitalized.
Incorrect: 2-methyl-1-propanol is often used as a solvent in chemical reactions.
Correct: 2-Methyl-1-propanol is often used as a solvent in chemical reactions.
2. Lack of spaces between numerals and units
Numerals and their units of measurement should be separated by a single space. Most peer reviewers will not comment on something that seems as minor as a missing space. But this is easy to fix, and that extra space does improve overall presentation.
Incorrect: First, 10mL of the sample was added to the reaction mixture. A 10% change in temperature was observed.
Correct: First, 10 mL of the sample was added to the reaction mixture. A 10% change in temperature was observed.
Just remember that the one definite exception to this rule is the unit for normality (N); this is typed closed up to the numeral (that is, without a space) so that it can be distinguished from Newton (also N). Another possible exception is the degree Celsius (°C). Some authorities require a space, whereas some require it closed up to the numeral; check which style your journal prefers.
Note that the percentage (%), degree (°), and prime (′) signs are not units and are set up close to the numerals they follow (e.g., 20% increase, an angle of 5°, and 5′-end).
3. Illogical representation of units
Because of oversight, authors can make some silly and obvious errors in units. A careful proofread can eliminate these.
Incorrect: The area of the sheet used was 9 × 6 mm2.
Correct: The dimensions of the sheet used were 9 × 6 mm.
Note that this is acceptable only when the unit is the same for each dimension.
Also correct: The dimensions of the sheet used were 9 mm × 6 mm.
Also correct: The area of the sheet used was 54 mm2.
The original sentence is erroneous because mm2 is the unit for total area. What the author intends to provide here is not the total area but the individual dimensions of the interface, i.e., the length and width, which should be represented in mm, not mm2.
Here’s another example:
Incorrect: The flow rate was 10 mL-1·min-1.
Correct: The flow rate was 10 mL·min-1.
A negative exponent should be used to imply units derived by division; therefore, its use with min is fine. The unit in the original sentence would read as “10 per mL per minute,” when the correct unit would be “10 mL per minute.” There should be no negative exponent for mL. This error is mostly due to oversight rather than incorrect understanding of unit representation.
4. Unnecessary expansion or abbreviation of units
The only time when a unit should be spelled out in full is if a sentence begins with a number followed by its unit or if it is being used without any accompanying number. See the examples below to understand these rules.
Incorrect: Nine N-m of torque was applied.
Correct: Nine newton-meter of torque was applied.
Better: We applied 9 N-m of torque.
The original sentence appears odd and confusing. While the second one is correct and easier to understand, the best solution is to revise the sentence such that both the number and unit appear elsewhere in the sentence.
Incorrect: The velocity was measured in m/s.
Correct: The velocity was measured in meters per second.
Here, the author is not reporting a value but just mentioning the unit. So it is incorrect to use the abbreviation.
5. Incorrect subject-verb agreement with units
An exception to the rules of subject-verb agreement is that a unit should be treated as singular, not plural, even though it is written and read out as plural. In non-scientific writing, the usual rules of subject-verb agreement may be followed for units as well.
Example: In order to produce 1 kg of aluminum, approximately 6.25 kg of recycled cans are needed.
As per the rules of subject-verb agreement, since “cans” is a countable noun, it should take the plural verb “are.” However, in scientific writing, units of measure are treated as collective nouns; hence, the usual rules do not apply. So, whether a unit is abbreviated or spelled out (mg or milligrams), the verb used would be “is” or “was” rather than “are” or “were.”
Therefore, in scientific writing, the correct usage would be as follows:
Example: In order to produce 1 kg of aluminum, approximately 6.25 kg of recycled cans is needed.
Here’s another example:
Incorrect: In this experiment, 2 mg of the extract were dissolved in 20 mL of water.
Correct: In this experiment, 2 mg of the extract was dissolved in 20 mL of water.
Here, even if you read “2 mg” out as “two milligrams,” you would use the singular verb “was.”
Now that you know the errors researchers commonly make, please be extra careful to avoid these in your paper. In addition, here are some stylistic guidelines that you will find helpful:
- Representing a range of numbers: It is common practice to use the en dash symbol (–) to represent a range of numbers. There are no spaces between the numbers and the dash (e.g., 5–8 days, 10–15 mL, 40%–45%)
- Punctuations allowed for representing numbers: Although there is no definite rule, some journals and style manuals insist upon use of only the decimal point in a number. For large numbers, groups of three digits separated by spaces are suggested instead of using commas (e.g., 1,200,345.67 is represented as 1 200 345.67 to avoid confusion over reading a large number as multiple numbers separated by commas).
- Casing requirement for units: Always crosscheck the accurate form of a unit to avoid incorrect/illogical representations. For example, the lowercase letter “k” is a prefix for the term “kilo”, whereas the uppercase letter “K” represents the unit “kelvin”.
- Spelling out units named after a person: When spelling out units named after a person, the name is always written in lowercase letters, but the symbol is capitalized and always in singular form (e.g., ampere à A, kelvin à K, weber à Wb, newton à N).
- Inline representations of compound units: Many journals insist upon specific styles for representing units. Compound units are represented as either fractions (using the solidus symbol “/”; e.g., mL/min, kg/s) or exponentials (e.g., mL‧min-1, kg‧s-1). For terms involving multiple primary units, please be sure to always check the appropriate representation or use parentheses as needed to avoid inaccuracies (e.g., watt per meter per second can be written as W/(m/s) or W‧m-1‧s-1 instead of W/m/s).
Now that you are aware of these errors, make sure you avoid them and present your data with utmost clarity. In addition, ensure that you follow the conventions of your field as well as any specific guidelines that your journal may have with regard to the representation of numbers and units of measurement.
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