I am trying to figure out how to calculate the change in concentration of an object within a volume, when you increase that volume. For example...
Let's say we have 5 flies per cubic centimetre of air.
Therefore, this would be 5,000,000 flies per cubic meter of air.
These are $5cm^{-3}$ and $5 \times 10^6m^{-3}$
Am I correct in my thinking? Also, how would I go on to figure how many flies there would be in say a km$^{-3}$ (cubic kilometer).
Using dimensional analysis:
$$\dfrac{5 \textrm{ flies}}{(1\textrm{cm})^3} * \dfrac{(1\textrm{cm})^3}{(10^{-2}\textrm{m})^3} = 5*10^{6} \textrm{ flies} \textrm{ m}^{-3},$$
which is valid because by definition $1 \textrm{ cm} = 1*10^{-2} \textrm{m}.$ Apply the same mentality to the second question, and you will be able to get the answer.