Step 1 :The question is asking which of the given metric relationships is incorrect. To solve this, we need to know the correct metric relationships.
Step 2 :1 milligram (mg) is equal to 0.001 grams (g), not 1,000 grams.
Step 3 :1 deciliter (dL) is indeed equal to 100 milliliters (mL).
Step 4 :1 kilometer (km) is indeed equal to 1,000 meters (m).
Step 5 :100 centigrams (cg) is indeed equal to 1 gram (g).
Step 6 :1 liter (L) is indeed equal to 1,000,000 microliters (µL).
Step 7 :So, the incorrect relationship is '1 milligram = 1,000 grams'.
Step 8 :\(\boxed{\text{The incorrect metric relationship is '1 milligram = 1,000 grams'}}\)