# Finding parts per million (ppm)

Everyone gets very confused when they try to learn how to convert from \(\textrm{g}/\textrm{l}\) or \(\textrm{mg}/\textrm{l}\), or \(\textrm{mg}/\textrm{g}\), or something similar, to \(\textrm{ppm}\). However, the process is almost identical to finding a percentage. To find a percentage (parts per hundred), you take the part, and the total and do the following:

\[\textrm{percentage of part in total} = \frac{\textrm{part}}{\textrm{total}}\times 100~\%\]

To find ppm (parts per million), you take the part, and the total and do the following:

\[\textrm{parts per million} = \frac{\textrm{part}}{\textrm{total}}\times 1~000~000~\textrm{ppm}\]

Notice any similarities there?

For example, suppose after a fire we have \(1~\textrm{g}\) of carbon in every litre of water in some pond. (I don’t know if this is realistic… =P) We first convert everything to the same units. \(1~\textrm{litre}\) of water is approximately \(1000~\textrm{g}\). Now, we can find the percentage of carbon in the water:

\[\textrm{percentage} = \frac{1~\textrm{g~C}} {1000~\textrm{g~H$_{\textrm{2}}$O}} \times 100~\% = 0.1~\%\]

And the ppm of carbon in the water:

\[\textrm{ppm} = \frac{1~\textrm{g~C}} {1000~\textrm{g~H$_{\textrm{2}}$O}} \times 1~000~000~\textrm{ppm} = 1000~\textrm{ppm} \]

Simple right?