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### Zero Before the Decimal Point?

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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.

Thanks.
Joe Bouril
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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)

"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/
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Associated Topics:
Elementary Fractions