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Q. Can an ellipsis be used instead of a period at the end of a complete sentence?
A. Yes, it can . . . But keep in mind that there are at least two ways to use an ellipsis. In the first of these, an ellipsis represents a lapse of some sort—for example, a faltering, a trailing off, or a pause. For that kind of ellipsis, use only three dots wherever the ellipsis occurs (as at the start of this answer).
But when the dots represent an omission within a quotation, retain a period at the end of a grammatically complete sentence. Put this period before the ellipsis, even if that’s not where the sentence ends in the original source: “Vanity and pride are different things. . . . Pride relates more to our opinion of ourselves, vanity to what we would have others think of us” (Jane Austen, Pride and Prejudice).