A sample must not contain more than 2% contaminants to be pure. Are there instances where 2.12% is ok?

I do not have any background in chemistry, I am asking this on behalf of someone else, twice translated, so I really hope it makes sense.


"A maximum of 2%" seems quite a clear specification, but since practice involves rounding of measurements and significant decimals, that might not be the case.


It may seem silly but which of the following options are valid work protocol?


1. *at most 2%* means less than 2.5% after rounding
2. *at most 2.0%* means less than 2.05% and option 1 still holds
3. *at most 2%* is the same as *at most 2.0%* and means at most 2.000...%




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Off topic: An optimal answer would be in the context of the EuAB ([Europäisches Arzneibuch](https://de.wikipedia.org/wiki/Arzneibuch)).




It depends mainly on the accuracy of your measuring instrument in practice and the accuracy required by your work.
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For example:


If you want to make a solution with 2g solute in it, and to measure amount of solute you have an measuring instrument that have least count of 0.1g, then 2.05g is acceptable as the instrument will show 2.0g only but if the least count of intrument is 0.01g then 2.05g is not acceptable if you want 2g.


In real life the least count varies for different situations.


For example if you are manager of a water bottle manufacturing unit you won't need much accuracy to fortify the water with minerals, but if you are carrying out a titration in lab to find strength of some oxidising agent you need very high accuracy that is why burette are made such accurate.


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It depends....


The statement *"A sample must not contain more than 2% contaminants to be pure"* is ambiguous as you have pointed out. To understand exactly what that means requires further clarification. 


First if expressed as 2% contaminants I'd expect that anything less than 2.5% would be acceptable. The point being that 2.0% contaminants is really a more stringent quality goal. 


The statement *"at most 2% contaminants"* brings in a different sort of flavor to the problem, and gets closer to reality. As a supplier I don't to buy or manufacture 99.9% pure chemicals and then sell them to you as a lower grade 98% pure. As a buyer I don't want to pay a premium for 99.9% purity if I could buy 98% purity for less and that purity would be acceptable to my processing. This is the classic buyer/seller problem related to "Acceptance sampling."


The gist of *[Acceptance sampling](https://en.wikipedia.org/wiki/Acceptance_sampling)* is that generally the whole batch can't be analyzed. In other words samples are taken from a batch of some chemical and just the samples are analyzed, not the whole batch per se. (After all you want to have something left to sell or use.) Now there are obviously errors due to sampling and errors due to analysis. The gist is that I find that the sample has 1.92% contaminants. However let's say that the standard deviation is 0.33%. So it is probable that the batch does have less than 2% contaminants, but there is a some chance that the batch actually exceeds 2% contaminants. So the [confidence interval](https://en.wikipedia.org/wiki/Confidence_interval) of any particular analysis should also be specified for a more complete specification. 


In fact if I were buying a lot of a chemical I'd probably have a contract that detailed how my acceptance testing would be done and under what conditions I could reject the whole lot at no cost to myself. So to write a less ambiguous specification requires some careful consideration. 


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