Do Decimals Bounded Between 0 and 1 (inclusive) Need a Leading Zero?

For a variable bounded between 0 and 1 inclusive, [0,1], should I use a leading zero when quoting a number?

E.g. the probability of rain is 0.5 or .5 (I realize this should technically be 50%, but I hope you accept the premise of the question).

And obligatory apology for the likely quite straightforward answer (a coauthor and I disagree), and thanks for whoever helps.

• Is the omission of leading zeroes an american thing? I have only encountered it in US literature and software. It is completely unheard of in Swedish, and I have not read enough British technical literature to see any trend in it. Commented Aug 19, 2014 at 12:12
• My coauthor and I are both american. Commented Aug 23, 2014 at 22:47
• @Ahlqvist As an American, the leading zero is typically dropped in short hand math, and white space preceding a number is treated as a zero. There are also occasions where a leading zero might dropped when denoting cents if a dollar sign is present (i.e. \$.50) but that is usually on hand written price tags used in more small mom and pop operations than in actual retail. Commented Sep 15, 2022 at 15:23

4 Answers

Unless you have a very good reason not to, you should include the leading zero. The combination of leading zero and decimal point is far more recognizable than the decimal point by itself.

The Chicago Manual of Style says that the inclusion or omission of a leading 0 depends on whether quantity could be greater than 1.

If the quantity could be greater than than 1, include the leading 0. Especially if quantities greater than 1 appear in the same context.

For quantities that are always less than 1, it is typical to omit the leading 0. CMoS gives several examples: Probabilities and baseball batting averages.

Odd choices of examples, given that 1 is a perfectly valid value for probabilities and batting averages. Likely they meant "never greater than 1. Coulda used better editing.

Other style manuals may give other advice.

• I don't understand remark about the choice of examples. I didn't lookup the CMoS, but you yourself already wrote that it said "could be greater than 1". The negation of that is already "never greater than 1", isn't it? Commented Aug 19, 2014 at 7:26
• APA says the same (depending on whether can be greater than 1).
– user5645
Commented Aug 19, 2014 at 10:15
• This makes sense. I never thought about probabilities and baseball scores, but you're right; those don't need leading zeroes. Otherwise yes, use one. Commented Aug 19, 2014 at 10:16
• Hagen, that was me trying to be snarky, and being clumsy with my wording instead. The exact phrasing of section 9.21 (about omission of the zero) begins: "If a quantity is always less than zero, as in probabilities, ..." That section also gives baseball batting averages as an example of such a quantity. Commented Aug 19, 2014 at 20:35

This guy is from Drexel, so he must be right: use the leading zero. Link

I found one quote on that site especially interesting, since it implies that the leading zero was customarily left out in the English system of units, but was strongly urged in the metric system of units.

"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."

Perhaps the leading zero is especially important in Europe (birthplace of the decimal system), where many write decimals using a comma: 0,81 mm.

Ex: The length is small ,81 mm.

What is the error? Is there a missing comma, or is the comma misplaced? See how confusing that is, without the leading zero?

Chicago manual of style makes exceptions and allows omitting zeros preceding the decimal point for batting average and rifle calibers. They should also allow an exception for inch decimal dimensions which never have a preceding zero if written correctly.

"ASME Y14.5 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."

If writing about engineering drawings in a company standard or a published journal do it properly. Example Inch .25±.05 and Millimeter 0.8±0.02 Otherwise you are leading people astray.