Is it an abuse of notation to omit the leading zero in a decimal less than 1?
Solution 1:
Depends on your style guide.
- 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).
Solution 2:
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 $1$.
Solution 3:
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...