Since ten times onehundred is onethousand, there are ten millimeters in a centimeter. But you asked how many milliliters are in a centimeter. A milliliter is a measure of volume and a centimeter is a measure of length so they are units that measure different quantities. It is like asking how many gallons are in a foot.
· One gram of water by definition is one milliliter volume. So if the liquid is close to the density of water then there will be a thousand milligrams in one milliliter. Since you are advised to give mg, the medicine must be very dense or else someone is confused in giving you directions. Wait till you can talk with the vet.