The thing you have to realize with this type of conversion is that you are converting mass to volume, meaning each conversion will be different depending on the substance you are converting. By converting first mg(mass) -> mL(volume) you can easily convert mL to cc(also a volume)
Many places will use a standard, such as water, when doing a conversion like this. For water it's easy 1 mg is 1 mL which is 1 cc. As a
surgical tech you will need to determine how the hospital does it's conversions. :D