In the language of food labels zero sugar should mean zero sugar. No matter how many servings you take. If you consume 3 servings of zero sugar, by common sense your body took in no sugar. Think about it:
0 x 3=0?
As per the FDA a food product can be labeled as 'Zero Sugar' if it has less than 0.5 grams of sugar. (refer to the sectioned below pulled from FDA - Code of Federal Regulations). When we consume multiple servings of "zero sugar" food products we do not end up metabolizing zero sugar. So in the case mentioned earlier consuming 3 servings of "zero sugar" does not mean you had zero sugar.
0 x 3 does not equal 0.
Because 3 servings of a "zero sugar" product could legally have has much as 1.5 grams of hidden sugar in it.
Due to all of this confusion reading and understanding labels is very important, we need to see what is the serving size to help us keep the zero sugar food products working and not throwing us off ketosis. See the example below: Sparkling Ice bottle is marketing themselves on "zero sugar" label, however if we see the label, we can notice one bottle has 2 servings. If we drink the whole bottle then we are no longer consuming zero sugar.
FDA Code of Federal regulations: Sugar content claims --(1) Use of terms such as "sugar free," "free of sugar," "no sugar," "zero sugar," "without sugar," "sugarless," "trivial source of sugar," "negligible source of sugar," or "dietarily insignificant source of sugar." Consumers may reasonably be expected to regard terms that represent that the food contains no sugars or sweeteners e.g., "sugar free," or "no sugar," as indicating a product which is low in calories or significantly reduced in calories. Consequently, a food may not be labeled with such terms unless:
(i) The food contains less than 0.5 g of sugars, per reference amount customarily consumed and per labeled serving or, in the case of a meal product or main dish product, less than 0.5 g of sugars per labeled serving; and
(ii) The food contains no ingredient that is a sugar or that is generally understood by consumers to contain sugars unless the listing of the ingredient in the ingredient statement is followed by an asterisk that refers to the statement below the list of ingredients, which states "adds a trivial amount of sugar," "adds a negligible amount of sugar," or "adds a dietary insignificant amount of sugar".