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?
 A: 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 $1$.
A: 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...  
A: 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).

