1. How many mg are in 24.5 ounces?
ANSWER: 6.95 x 10⁵ mg

Solution Worked Out

There are many different ways to do this problem which will depend on the equivalences that you use. First, we define the given and the desired units.

Given: 24.5 oz. and Desired: mg

I can go from grams to mg. I also know there are 454 g in 1 lb and 16 oz. in 1 lb. I am going to use three equivalences:

16 oz. = 1 lb, 1 lb = 454 g, and 1 g = 1000 mg
My roadmap will look like this:
\(\mathbf{ oz.\;\rightarrow\;lb.\rightarrow\;g\rightarrow\;mg}\)

I will use three conversion factors, one for each of the arrows in the road map. My 6 conversion factors follow (remember, we can write two conversion factors for each equivalence):

\(\displaystyle\frac{16\;oz}{1\;lb}\quad or \quad \frac{1\;lb}{16\;oz}\)
 
\(\displaystyle\frac{454\;g}{1\;lb}\quad or \quad \frac{1\;lb}{454\;g}\)
 
\(\displaystyle\frac{1\;g}{1000\;mg}\quad or \quad \frac{1000\;mg}{1\;g}\)
 
Now, we can set up our problem. We start with the given which is 24.5 oz. Looking at the roadmap, we need to convert from ounces to pounds. We use the conversion factor that will cancel out ounces. We then want to go from pounds to grams using the conversion factor that will cancel out pounds. Finally, we convert from grams to mg. We use the conversion factor that will cancel out g and leave us with mg. The calculation follows:

\(\displaystyle\require{cancel}24.5\cancel{oz}\times\frac{1\;\cancel{lb}}{16\;\cancel{oz}}\times\frac{454\;\cancel{g}}{1\;\cancel{lb}}\times\frac{1000\;mg}{1\;\cancel{g}}\;=\;\mathbf{6.95\times{10^5}\;mg}\)
 
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