Voyager's Hometead is one episode that gives us both the calendar date and stardate. Therefore, April 5 2378 is apparentally stardate 54868.6.
Like an impressionist painting -- if you look at it up close, you can see how rough the brush strokes are and how little it resembles reality, but you're not supposed to look at it up close; you're just supposed to look at the broad strokes and get a general feel for what it's trying to convey.
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