2. How many ng are in 43.6 mg?

 Answer: 43600000 ng or 4.36 x 10⁷ ng

Solution

There are 10⁶ ng in 1 mg. If at first we missed that fact, we can set up equivalences. What do we know about ng and mg? Well, we know that there are 10⁹ng in 1 g and 10³mg in 1 g. This is a difference of 10⁶. We can write the equivalence, 10⁶ng = 1 mg. This will allow us to convert from 43.6 mg to ng. We write the conversion factor so that mg cancel out. Using this we have:
\(\require{cancel}43.6 \cancel{mg}\times\frac{10^{6}ng}{1\cancel{mg}}\;=\;43,600,000 = 4.36\times10^{7}ng\)
You can also do this problem using the following two equivalences: 10⁹ng = 1 g and 10³mg = 1 g. Using these we get:

\(43.6\cancel{mg}\times\frac{1\cancel{g}}{10^{3}\cancel{mg}}\times\frac{10^{9}ng}{1\cancel{g}}=43600000 \;ng = 4.36\times10^{7}ng\)

We could have also used the following equivalences: 10^-9g = 1 ng and 10^-3g = 1 mg. Using these we get:

\(43.6\cancel{mg}\times\frac{10^{-3}\cancel{g}}{1\cancel{mg}}\times\frac{1\;ng}{10^{-9}\cancel{g}}=43600000 \;ng = 4.36\times10^{7}ng\)

As you can see, there are many different ways to do these problems. It is up to you to become familiar with the equivalences and use them to convert between units. Make sure you know the prefixes from the table and the value each prefix corresponds to. Once you commit these to memory, and with practice, you will be able to solve any type of conversion problem. The key is to work many problems. Once you do, they will become second nature.

Go to Next Exercise
Go Back to Measurement, Metric System, SI Units
Go to General Chemistry 1 Study Guides