Last time we ended with questions about writing (or ignoring) zeros at the end of a decimal. I didn’t have room for one more question, so I’ll put it here.
This question comes from 2000:
Zero Before the Decimal Point? A fellow instructional designer and I are having a philosophical dispute over the purpose and philosophy of textbooks and teachers showing the zero in front of a decimal number. (I have a teaching certificate and an M.A. in instructional design, while he has a Ph.D. in math.) "0.34 x 0.298 =" or "0.562 / 0.25 https://web.archive.org/web/20010223022201/http://www.westmead.nsw.gov.au/alliedh/pharm/pages/goodpres.htm">http://www.westmead.nsw.gov.au/alliedh/pharm/pages/goodpres.htm "Never leave a decimal point naked, such as .5 mL. When the decimal point is not seen, a tenfold overdose may occur. "When a decimal fraction must be prescribed, always write a zero before the decimal point. "Never put a decimal point and zero after a whole number such as 2.0 mg. This should be written as 2 mg. If the decimal point is not seen, a tenfold overdose may result."
This last example is clearly important in this context, but inappropriate in contexts where significant digits matter, as in engineering. The zero at the end, in such contexts, does mean something, and is not there just to hold a place.
Again, Medicine, Malpractice and the Law (a paper by Raymond Wacks) http://www.medicine.org.hk/bma/programme.htm "The expression of drug dose and units should be clear. For whole numbers it is better to avoid following with a decimal point and a zero which may be misinterpreted as ten or one hundred times the appropriate dose. For numbers less than one it is essential to place a zero before the decimal point."
Here is an interesting current discussion of the real possibility of such errors, from Preventing 10-Fold Dosage Errors in Pharmacy Times:
The risk of 10-fold overdoses is made greater by health professionals and computer systems that dangerously use trailing zeros (eg 1.0 mg, which can be misread as 10 mg) or by health care workers who do not use leading zeros (eg .5 mg instead of 0.5 mg, the former of which can be misread as 5 mg). …
Similarly, in product labels: FDA Guidelines (U.S. Government FDA/ORA Compliance Policy Guides) http://www.fda.gov/ora/compliance_ref/cpg/cpggenl/cpg140-500.html "A zero before the decimal point should be used in numbers between 1 and -1 to prevent the possibility that a faint decimal point will be overlooked. "Example: The oral expression "point seven five" is written 0.75."
This is essentially the same as medical concerns. These guidelines are currently found at CPG Sec.140.500 Metric Declarations of Quantity of Contents on Product Labels (Supplemental Guidance 3G).
Next, in the metric system: Metrics the Right Way (George Sudikatus, ICF KH Metric Coordinator, Pacific Northwest National Laboratory) http://www.pnl.gov/ag/usage/metrics.html "In the United States, the standard decimal marker is a dot on the line (i.e., a period or 'decimal point'). When writing numbers less than one, add a zero before the decimal marker. For example, on a drawing you might define a small length in English units as .032 in., but write the metric length as 0.81 mm."
Many people don’t know how much is specified in various government and international rules about the metric system standard! Here, they don’t care how you write inches, but they want metric measurements to be written in a way that maximizes clarity.
A standard U.S. guide for the metric system (from NIST) is Writing with Metric Units:
The dot or period is used as the decimal point within numbers. In numbers less than one, zero should be written before the decimal point. Examples: 7.038 g; 0.038 g.
Also, some publishers and organizations include it as part of their style guides: Instructions for Authors (Publisher: Taylor and Francis Group) http://www.tandf.co.uk/journals/authors/t-authors/wstauth.html "Use a zero before the decimal point for numbers less than one. For example: t = 0.40 "However, do not use a zero before the decimal point when the number cannot be greater than one. This occurs with correlations, proportions and levels of statistical significance. For example: r = .27, p < .01
This is interesting: They imply that when context makes it clear that there will be a decimal point (27 would make no sense for a correlation coefficient), you can leave out the zero – and in fact, should.
The same rule is used in APA Style, here in their Numbers and Statistics Quick Guide:
But some take an opposite position:
On the other hand (!): Preparing Manuscripts for Demography (Department of Demography, Georgetown University) http://www.georgetown.edu/departments/demography/main/Student/demo.htm "Decimal fractions should not include a zero before the decimal point (e.g., .05 is correct; 0.05 is incorrect)."
They give no reason, and I can’t find any remnants of this opinion now. But I did discover a drafting standard, ASME 14.5, that says (about inch measurements only, not metric),
1.6.2 Decimal Inch Dimensioning
The following shall be observed where specifying decimal inch dimensions on drawings:
(a) A zero is not used before the decimal point for values less than 1 in.
This leaves us with two exceptions to the rule: In statistics, don’t use the leading zero for numbers restricted to the interval \((-1, 1)\), and in drafting, don’t bother with it except for metric measurements.
These are not carefully chosen references, just those that I found in a quick search. They should suggest that inclusion of the zero is a common, though perhaps not universal, practice, and has good reasons behind it. Therefore, I think it is appropriate for students to become familiar with this style. We can let them become lazy later - if they don't become pharmacists. On the other hand, I don't think I would require them to always put in the zero themselves; and I would make sure they saw numbers written without the leading zero to make sure they knew it meant the same thing.
This last pedagogical comment is important. Students should learn this “rule” not as a mathematical requirement (as if .45 did not mean the same thing as 0.45), but as a matter of good style to prevent human error. They will see both forms in the real world, and should be able to read them (without a compulsion to pull out a red pen and write in the zero), even if they rarely write decimals without the zero.
For a concurring opinion from 2005, see:
Agree with the conclusion but, we need to be clear that the environment (regulated or not regulated) will define the practice. I also believe in the preparation of people for the worst example specially when you may be performing under a regulated environment. Your discussion was clear and well done.
Linda WrightI vote for the leading zero. In the chemical industry it’s too easy to overlook the decimal, especially when COA’s are faxed or copied numerous times. I have also observed that folks that are not used to mathematical calculations will miss the decimal and miscalculate analytical results. American Chemical Society Style Guide recommends zero before the decimal.
MegumiI believe that it is a common international scientific standard to use the leading zero (except specific cases, some of which you mentioned). I grew up in Japan and I had never seen a naked decimal point until I came to the US in the 80s. I found it shocking, lazy (in the typical judgmental manner of a teenager) and error-prone. I understand now that it is a long-standing tradition, especially in certain trades. My husband is an American engineer and he uses the leading zero to avoid errors. Another American engineer acquaintance of mine (and an educator) does not use it. I wish he would for pedagogical reasons. I also teach science and I often have to decipher my student’s writing without the leading zero (and a miniscule decimal point). Surely the students make mistakes that are avoidable by putting an unequivocal zero in front.
I begin to feel that I must side as passionately with the leading zero as I do for the Oxford comma! -Educator in North Carolina
Blake HundleyI spend a lot of time reading close tolerance drawings and I am of the opinion that for decimal inch dimensional call outs there should be no leading zero ever. For metric callouts always. Not using a leading zero has nothing to do with laziness and I can only laugh at this notion. I would say it could be equally lazy to use a leading zero because it indicates that you are too damn lazy to look for the decimal. a lead zero means zero and a lead decimal indicates less than one. Why do I need to be looking at a big zero that indicates less than one when the decimal has already done so. It just makes 0.00% sense.
Dave PetersonYes, as already indicated, this is standard in trades using decimal inch measurements. If you are used to it, then it will make perfect sense not to use the decimal. (Though in the last link in the article, Doctor Rick comments, “I have run into trouble trying to read measurements in plans that were faxed to me, when the sender did not put in the zero: for instance, 2′ .5″ looked like 2′ 5″ so I made something 4.5 inches too long.”) For fun, I asked ChatGPT, “Why do we not put a leading zero before a decimal point for decimal inch measurements?” Parts of its answer made little sense, but it concluded,
This convention has been in use for a long time, and people are accustomed to it. It’s part of the standard practice in many industries and trades where inch measurements are common. While this convention is particularly prevalent in the United States, it’s also followed in many other countries where imperial units are used. Maintaining consistency with international standards helps in communication and comprehension across borders. Overall, while there’s no strict rule against using a leading zero before a decimal point in inch measurements, the convention of omitting it has become deeply ingrained in practice due to its clarity, simplicity, and historical precedence.
On the other hand, when I asked it, “Why do we put a leading zero before a decimal point for metric measurements?”, its conclusion (again, following some nonsense) was,
The use of a leading zero before the decimal point is part of the International System of Units (SI) conventions. It helps maintain consistency in notation across different countries and disciplines, facilitating clear communication and avoiding confusion. Using a leading zero helps to avoid ambiguity, especially in handwritten or typed documents where a decimal point might be mistaken for a punctuation mark. The leading zero clearly distinguishes the decimal part of the measurement. When performing calculations involving metric measurements, having a consistent format (i.e., leading zero before the decimal point) helps maintain precision and accuracy, as it ensures uniformity in numerical representation. Overall, the use of a leading zero before a decimal point in metric measurements is a standardized practice that enhances clarity, consistency, and precision in communication, calculation, and interpretation of measurements within the framework of the International System of Units (SI).
Ultimately, you do what communicates best with those you are working with. When in an industry, do as people around you do. I see no other reason than tradition to handle this differently in the two systems of measurement; on the contrary, it would seem to me that in metric, you could just rewrite .1 cm as 1 mm and avoid the issue, while this is difficult with inches. I’d be very interested in specific ideas about this.
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