What determines how precise a measurement is
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because of the mass
Yes it is possible. 21.354 inches is very precise but could be inaccurate.
Synonyms of "specific" and "precise" include accurate, detailed, explicit, stringent or rigorous. A precise measurement is one made with well-maintained equipment and using the correct methods in a careful manner.
The term "precise" refers to the range of measurement to which a value is calculated. The term "accurate" implies that the measurement value is essentially correct, to within some range of error.However, the terms are often used synonymously, since "precise" has the desired quality of being exact, which in some cases is a separate concept from accuracy.
An accurate but not precise measurement would be an approximate measurement. For example, in cooking or baking, the ingredients list might indicate one cup of a certain item. Scientifically, however, one cup, (or 8 ounces) would not be a precise measurement for testing purposes. Instead, a precisemeasurement would be required, especially when the results of a specific test need to be reproducible and the quantities are minute, as in micrograms, for example. Accuracy in measurement is of closeness to the actual or exact, but precision in measurement is closeness to the same spot each time it is taken.