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I'm trying to figure out how to divide a medicine up by millions of units into grams or half grams and figure a group like this who play with various math problems might be able to help:

What I know about it: comes in a container labeled '1BU'

Net Weight is '153 grams'

Potency is '6536 I.U./mg'

Trying to figure out how to convert 3 million units to grams or percentage of grams. Told it maybe .45 grams. Sound about right? Thanks

jordanbrianjason126
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  • $6536$ units per mg means $6,536,000$ units per gram which means $1,000,000$ units in $0.15299$ grams and hence 3 millions units in $0.45899$ grams – Anvit Jan 13 '19 at 04:10
  • 1BU = 1 billion unit = $10^9 {\rm unit} = 153{\rm g} \implies 3 \times 10^6 {\rm unit} = 153\times \frac{3\times 10^6}{10^9} = 0.459 {\rm g}$ – achille hui Jan 13 '19 at 15:22

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Anvil has already given a correct answer in a comment, but here is the calculation in more detail.

Here is how I was taught to do such calculations, long ago:

$$\require{cancel} \frac{3,000,000 \cancel{\text{ IU}}} {6,536 \cancel{\text{ IU}} / \cancel{\text{mg}} \times 1,000 \cancel{\text{ mg}}/\text{gm}} = 0.4590 \text{ gm}$$

The idea is to treat the units of measurement as if they were algebraic variables; so IU in the numerator cancels the IU in the denominator, then the /mg and mg in the numerator cancel, leaving /gm in the denominator. Finally, $$\frac{1}{1/\text{gm}} = \text{gm}$$ so the unit of measurement of the final result is gm. The rest of the calculation is just arithmetic. The only fact you have to know beyond what is in the problem statement is the conversion factor of 1,000 milligrams per gram.

awkward
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