Question

If you were asked to convert 25 mg to the unit hg, which of the following would be the first fraction used in the conversion

Answer 1

Your first step is to get rid of the milli (m) prefix. An easy way to do this is to remember that m = 10^-3. Therefore 25 mg = 25 x 10^-3 g = 2.5 x 10^-2 g. Now you need to get to hectograms (why? that's a weird unit!) Since h = 10^2, you need to rewrite your measurement so there is a 10^2 in front of the g:

2.5 x 10^-2 g = 2.5 x 10^-2 x (10^-2 x 10^2) g = 2.5 x 10^-4 x 10^2 g.

Now just replace the 10^2 g with hg, and you get 2.5 x 10^-4 hg.

That way works even in your head, but the more formal way uses units ratios, in which you continually multiply by 1 (which doesn't change the measurement), using various ways of writing 1. For example, you can write 1 as 10/10 or 123.4/123.4 or (which is relevant here) 10^3 mg / 1 g or 10^2 g / 1 hg.

To get rid of the mg, multiply by 1 in such a way that the mg cancel:

25 mg x (1 g / 10^3 mg) = 25 x 10^-3 mg = 2.5 x 10^-2 g.

That's the answer you want. To continue on to get the hg, multiply by 1 in such a way that the g cancel:

2.5 x 10^-2 g x (1 hg / 10^2 g) = 2.5 x 10^-4 hg.