Which metric relationship is INCORRECT?
1 milligram $=1,000$ grams
$1 \mathrm{dL}=100 \mathrm{~mL}$
$1 \mathrm{~km}=1,000 \mathrm{~m}$
$100 \mathrm{cg}=1 \mathrm{~g}$
1 liter $=1,000,000$ microliters

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 ：\(\boxed{\text{The incorrect metric relationship is '1 milligram = 1,000 grams'}}\)