What's the difference between premier and grand cru Burgundy?

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Dear Dr. Vinny,
What's the difference between premier and grand cru Burgundy?
—Bing, Singapore
Dear Bing,
There are four quality categories in the Burgundy classification system for white and red wines, which are made from Chardonnay and Pinot Noir, respectively. From least to most prestigious, they are regional appellations ("Bourgogne" is the broadest), village or commune appellations (such as Pouilly-Fuissé, Pommard or Nuits-St.-George), and the two levels of vineyard-specific designations, premier cru and grand cru.
The cru hierarchy can be confusing, because premier cru is below grand cru, even though the word "premier" translates as "first" and those wines are often abbreviated as "1er cru."
Grand cru–designated wines represent only about 1 percent of the total production of Burgundy, but this classification system, developed hundreds of years ago, isn’t a foolproof guide to quality. You may very well prefer a good grower’s premier cru to a neighbor’s grand cru, and there are plenty of terrific village wines. The only thing you know for sure is that grand cru wines are the rarest and, consequently, usually the most expensive.
—Dr. Vinny