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Can you say me please if it is correct to write $0,000$ or just $0$? I have to complete a table and there are decimal numbers, and I don't know how to do in the case I have an absolute zero.

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    That depends on what you are doing. By using a single $0$, one can easily identiy those when looking at a table. If that is the point ("Look at all the zero data-points I have in my table") then it's the way to go. – 2017-01-16
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    It depends. If your entries have to comprise $4$ digits, then you should write $0,000$. Since $0 = 0,000$, mathematically speaking, it doesn't matter what you put. – 2017-01-16
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    What's a zeccimal number? – 2017-01-16
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    Zeccimal numbers what do you mean? – 2017-01-16
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    I guess you mean decimal numbers? I don't think this is about measure theory, measure theory is related to integration theory. – 2017-01-16

4 Answers 4

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Mathematically they are equivalent.

However there are conventions about accuracy that make them different. When writing $0.000$ it is basically assumed that those written digits are correct, but there may be errors further down the expansion. That is it means something like $0.000\pm0.0005$ (or perhaps slightly larger error marigin).

On the other hand if you only write $0$ it might be interpreted as meaning exactly that (without any error marigin). However if you have error marigin on the other numbers it's likely that there's some error for the zero values as well and that they are not different from the other values (except they're close to zero). One should therefore probably use the same number of decimals there as for the other values.

Also in tables one should distinguish between the quantity $0$ and that there is no quantity (which is normally indicated by a dash).

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    I've even seen equations for models written as $f(x, y) = a*x + b*y + 0$, where each term a, x, b, y has an associated uncertainty but the 0 is explicitly and has an uncertainty associated with it, which is the uncertainty in the model parametrisation itself. – 2017-01-16
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One typically uses the same number of decimal places for all entries in the table, both for aesthetic reasons and to indicate the precision of the values if they are computed numerically.

One notable exception is as Laray suggests: zero written as "$0$" will stand out in the table if all other values have several decimal places.

Another exception would be if different groups are computed differently--for example, a column of population counts might all have no decimal places, while a column of average ages might have a couple of decimal places each.

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Since you mentioned a table in your question, One exception would be if you are using concatenation operations. In that case $0.000$ , $0$ and $0000$ may all be treated as different depending on the usage . This is because in the concatenation operations the place value matters. Otherwise, mathematically the face value of $0.000$ and $0$ is same.

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    No idea what you mean by "concatenation over the columns". – 2017-01-16
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    For instance I have 0.000 in one of the rows of first column and 5 in one of the riws of second column , then concatenating may result in 0.0005 – 2017-01-16
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    This is not peculiar to zeroes. The concatenation of $3.141$ with $5$ would also be flawed. – 2017-01-16
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    That's true I am just pointing out the instance when 0.000 may be incorrect to use in place of 0 – 2017-01-16
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$0,000$ cannot be taken wrong, it clearly denotes the value $0$. By the way, the same question holds for every trailing zeroes. F.i. $3,45000$ is all right for $3,45$.

Anyway, as said by @skyking, showing the trailing zeroes stresses that they are exact.