Canceling Units
Cancel the units in the following setup and give the unit of the final answer:
3.5\,{\mathrm{L}}\times{\frac{1\times10^{3}\,{\mathrm{mL}}}{1\,{\mathrm{L}}}}\times{\frac{0.48\,{\mathrm{g}}}{1\,{\mathrm{mL}}}}\times{\frac{1\times10^{3}\,{\mathrm{mg}}}{1\,{\mathrm{g}}}}\,=
All matching units in the denominator and numerator cancel to give mg as the needed unit for the answer.
3.5\,\cancel{\mathrm{L}}\times{\frac{1\times10^{3}\,\cancel{\mathrm{mL}}}{1\,\cancel{\mathrm{L}}}}\times{\frac{0.48\,\cancel{\mathrm{g}}}{1\,\cancel{\mathrm{mL}}}}\times{\frac{1\times10^{3}\,{\mathrm{mg}}}{1\,\cancel{\mathrm{g}}}}\,=\text{needed unit of mg}