How in the world does toothpaste work?
The typical tube of toothpaste weighs in at roughly 6.4 ounces. That's 181 grams (If you've got the larger 8 ounce tube, you're sitting pretty at 226 grams, but for the sake of this exercise we'll stick with the standard size tube).
The active ingredient is sodium fluoride. In a standard tube that active ingredient composes about .243% of the total mixture.
That means for every 100 grams of toothpaste there is .243 grams of sodium fluoride. So to figure out how many grams of active ingredient are in a tube of toothpaste we need to complete the ratio. Generously rounding .243 to .25, and 181 grams to 200, we can see that in a tube of toothpaste there is approximately half a gram of active ingredient.
Now I don't know about you, but I'd guestimate that my wife and I get about a good 100 uses out of a tube. (These guys figured out that a 6 ounce tube would get you about 113 uses, so I'm pretty sure that's a decent estimate). Assuming for a minute that the active ingredient is distributed throughout the tube in a perfectly even fashion, that means that in each of 100 brushes you should get .005 grams of sodium fluoride on your teeth.
Maybe it's just me, but that sure as heck doesn't seem like it'd be enough to accomplish anything. Even if you brush in a ridiculously thorough manner, I can't imagine you'd touch that tiny bit of sodium fluoride to all of your teeth. And considering that the active ingredient probably isn't distributed perfectly throughout the tube, from time to time you're probably brushing your teeth with completely non-active ("inert") ingredients.
So seriously, how does toothpaste work? I don't get it.
Something better than nothing