Zero Before the Decimal Point?

Date: 10/06/2000 at 09:22:14
From: Joe Bouril
Subject: Zero represented before the decimal

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 ="

As a former elementary teacher for 12 years, I contend that the zero 
is redundant to the decimal, is a harmful crutch, and can even be 
distracting. The prerequisite skills up to the decimal include mastery 
of place values, and the comprehension of the decimal point. However, 
I still see it used in classes past the fourth grade.

I agree with him that when used in a text sentence, it makes sense to 
distinguish punctuation. I also agree that when the decimal point is 
initially introduced, it can be used as a transition.

I disagree with him that when used in a stand-alone math problem, it 
is still visually pleasing and, I guess, therefore better for the mind 
to compute accurately.

Please explain and arbitrate.

Thanks.
Joe Bouril

Date: 10/06/2000 at 15:21:19
From: Doctor Peterson
Subject: Re: Zero represented before the decimal

Hi, Joe.

My main problem with your reasoning is that you evidently think that 
redundancy is bad; I think it's good. Take another example, the use of 
parentheses: There are many situations where we don't need parentheses 
because the rules make the meaning clear; yet I recommend putting them 
in, just to make it easier for the reader, and to ensure that if a 
rule is forgotten, it will be hard to misread it. (This is commonly 
recommended for good computer programming practice, where there are 
extra rules that are easy to forget.) Sure, one could use extra 
parentheses as a crutch, putting them in everywhere to avoid having to 
learn the rules at all; but that's only in the extreme. Crutches are 
useful to those who need them.

In the case of the zero before the decimal point, although it doesn't 
affect the value of the number, it is almost universally considered 
good practice to include it - not for mathematical reasons, but for 
human reasons. It can be easy to miss the decimal point, and the zero 
makes it stand out. It's not essential, but it's a good habit to 
develop for those occasions when clear communication will be 
necessary.

Just to make sure this was not my own quirk, I did a quick search for 
other people who might make the same - or opposite - recommendation. 
Here are a few:

First, in writing drug prescriptions:

   Good Prescribing Guidelines (Westmead Hospital Department of 
   Pharmacy - Khai Bui)
   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."

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."

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."

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."

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

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)."

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.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/