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Chapter 1, section 3, problem 12.
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The recommended daily allowance of trace metal magnesium is 410 milligrams per day.
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For males.
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And the question asks us, express this quantity in micrograms per day.
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So the first thing they recognize is just a unit conversion problem.
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And so they want us to go from the basic unit that we need to change is micro, a milligram.
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To micrograms, so this is a mu.
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You're written like this.
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Okay.
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And so one thing, one way that we can go about is to recognize that for one gram, we have a thousand milligrams.
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And in one gram, there's also 10 to the 6, or 1 million micrograms.
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And so when we want to do a unit conversion right here, we realize that there are, actually a thousand micrograms in a milligram we can get this by taking this quantity divided by a thousand on both sides and so you lose three zeros here three zeros here and that would be ten to the three which is a thousand so a thousand micrograms is one milligram and so we go four hundred ten milligrams a day until when we're converting units we just multiply by one and so in this case, we have our quantity here.
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And so we want mg on the bottom.
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So we divide both sides by milligrams.
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And we get this is equal to 1.
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And so as i mentioned, mg on the bottom, 1 milligram over, and we have 1 ,000 micrograms on top.
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And so we cancel out these.
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That equals 1, a milligram over milligrams equal to 1.
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We're left with microgram over per day and so the our answer is going to be 410 ,000 micrograms per day so this is for part a and so for part b this is for adults the recommended daily allowance of the amino acid lysine is 12 milligrams per kilogram body weight let's be at one kilogram of body weight so this is just a general unit we have our now and then it says how many grams per day should a 75 kilogram adult receive so we want to find out our quantity x grams per 75 kilogram body weight okay and so what we could actually do for this problem is we're gonna need to change this mg to g and then this bottom part this might seem a little weird but we're actually going to need this to be 75 kilograms body weight instead of just one and so we'll begin with the milligram conversion so we start off with the quantity here and so we want mg to be on the bottom and so we know for every gram we have 1 ,000 milligrams and then what we want to do is remember we can only multiply by one.
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And so how do we get the 75 here when we only have one? you basically multiply top and bottom by just 75.
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So these are you to cancel out.
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And we're left with 12 times 75 grams, 1000.
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And this is 75 kilograms body weight.
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And so this quantity is 900.
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And so we're actually left with 900 over 1 ,000.
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Is 0 .9 grams for a 75 kilogram body weight.
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And so that's how many grams a 75 kilogram adult should receive.
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Part c.
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This is a typical multivitamin tablet can contain 2 .0 milligrams of vitamin b to riboflavin.
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So we know for every tablet we have that much.
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Okay, it says the recommended daily allowance, 0 .003 grams per day.
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And so the question asks, how many tablets should a person take a day to get the proper amount of this vitamin, if he gets them from other sources? so what we want to find out is how many tablets per day are needed.
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And so you can see from all of our units right here, we basically have grams per day, and then we have milligrams and tablets.
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And so this is a quantity we want to find out...