# Is it an abuse of notation to omit the leading zero in a decimal less than 1?

Is it acceptable to write $.001$ rather than $0.001$ when using decimal notation?

Are there contexts in which omitting the leading zero is acceptable, and other situations in which it is not?

• They both mean the same thing, but the leading zero can help reduce error when reading the numbers. I know pharmacists, nurses, etc. prefer to include the leading zero to reduce the possible confusion between, say, 0.1 mg and 1 mg of a medicine. May 13, 2013 at 5:33
• It is understandable that's why people sometimes do not write that 0 and if there is another number then we definitely write May 13, 2013 at 5:34
• I am little bit curious about a geographical aspect of this question. My limited exposure is that the practice of dropping the leading zero is common in the US (think: baseball stats), but largely unheard of in Europe. I am prepared to be wrong about both of these sweeping generalizations. In fact, it is highly unlikely that the division would be this sharp, but I also think that the practice varies from one region of the globe to another. May 13, 2013 at 7:18
• You might want to make more precise why you consider this abuse of notation. As the term suggests, abuse of notation is using some existing notation for a purpose different from what it was originally intended for. That does not seem to be the case here. May 13, 2013 at 8:23
• @JyrkiLahtonen: Well, a strong factor for the dissemination of the missing zero in the world is the statistical software SPSS, which uses that representation itself since its occurence on the market by its tabular output as well as by the educational effect of this on the scientists who are using it - the missing-zero-style occurs in journal-articles as well as in books, when SPSS-output has been metabolized... ;-) May 13, 2013 at 8:28

• MLA Style requires the zero, as does US GPO style.
• APA Style uses the zero before the decimal point if and only if it's possible for the thing being measured to be greater than one. So a child could be “0.99 m” tall, but a probability could be “.99”.
• Wikipedia requires the zero except for sports statistics (e.g., Ty Cobb batted .366) and commonly-used terms (a .22 caliber gun).
• Dropping the zero in front of the decimal point is common in the US but not in the rest of the world.
– user46234
Dec 12, 2019 at 5:47

It is not an abuse of notation as long it is clear, though I would assume most people would prefer to write it as $0.001$. Of course, you could also write it as $00.001$ and some else might prefer to write it as $000.001$. In general, it is preferred to write it as $0.001$, especially if it is used in a sentence since . could be confused with period .. Also, when we write a number say $.1$, it might be possible that someone might miss the .infront of the $1$ and might read it as $1$. Whereas, if we precede the number with a $0$, then we give the reader a heads-up that since we have a zero infront, watch out for a number less than $1$.

• No shoulders of giants in your location? May 13, 2013 at 10:14
• @Gustavo It's Marvis. Haha
– P.K.
May 13, 2013 at 14:27

If I document matrices where there are systematic zeros, for instance in triangular matrices, then I even reduce the "0.0" to the single "." to help the reader to focus on the non-redundant, numerically relevant part.
$$P=\small \begin{bmatrix} 1 & . & . & . & . & . \\ 1 & 1 & . & . & . & . \\ 1 & 2 & 1 & . & . & . \\ 1 & 3 & 3 & 1 & . & . \\ 1 & 4 & 6 & 4 & 1 & . \\ 1 & 5 & 10 & 10 & 5 & 1 \end{bmatrix}$$ Also in correlation-matrices, where it is understood, that entries cannot have absolute values greater than 1.0 I feel it improves readability when ".1234" is written instead of "0.1234".
$$C= \small \left[ \begin{array} {rrrrrrr} 1. & - .078& - .135& - .084& - .015& .039\\ - .078& 1. & - .021& - .020& .020& - .010\\ - .135& - .021& 1. & .052& .052& - .012\\ - .084& - .020& .052& 1. & .063& .115\\ - .015& .020& .052& .063& 1. & - .057\\ .039& - .010& - .012& .115& - .057& 1. \end{array} \right]$$

As far as this two examples are concerned, I think that reduction is "acceptable" (and is also used in many instances in the literature).

But this reduction is unconvenient (and possibly in-acceptable) if there is a risk of misreading of numbers, for instance, where the decimal point might be overlooked and cannot be re-discovered (because of lack of systematic/redundant information) - and this is in my experience the usual occurrence of decimal numbers...

• I think the assumption that when writing a single period to represent zeros, this period is in fact a denuded decimal point is questionable. In fact my experience is that more often than not, one simply leaves the spot entirely blank; in cases where one does write a dot, it may be just to provide a visual guide for rows and columns in regions that would otherwise be completely blank. Certainly I would not expect to see a bare comma used anywhere by authors for who the decimal separator is a comma. May 13, 2013 at 7:56
• @Marc: Yes to the last aspect. The dot there is more a placeholder than the decimal-dot: in case of the latter it would suggest the false impression, that the missing number could have be meant as real/approximated float instead of integer type. In the lower triangular part of P I would not replace the zero by the dot, because it is not a systematic one. May 13, 2013 at 8:21
• I have exactly the opposite view: I find $0.1234$ more readable than $.1234$ in virtually all contexts. I don’t object to the points in your first example, but I also don’t consider them decimal points: they’re just placeholders. As further evidence of this, I’ve never seen a comma used instead, even by those from places where my height would be written $1,61$. May 13, 2013 at 18:00