Wouldn't you divide by 1000, not multiply, as you are talking about converting
Unparseable latex formula:
dm^-^3
to
Unparseable latex formula:
cm^-^3
? If you have 3000 moles per decimeter cubed then surely there would be 3 moles per centimeter cubed, not 3,000,000. I expect this is what was meant, but it could easily be misinterpreted.
As a side note you should really know how it works in case you forget what to do. 10cm=1dm. 103=1000. 13=1. Therefore 1000cm3=1dm3.