Units — Basic example

- [Instructor] A high school class is measuring the amount of nitrate in a local stream. To be considered safe to drink, the maximum amount of nitrate that can be present in water is 10 milligrams per liter. The class takes a sample of 15 liters of water. If the number of milligrams per liter of nitrate in the stream water is 3/4 of the maximum that is safe to drink, how many milligrams of nitrate should the class expect to find in their sample? All right, this is interesting. So in this sample, in this 15-liter sample, they find that the number of milligrams per liter of nitrate is 3/4 of the maximum. Well, what's the maximum? Well, they tell us up here. They tell us, let me underline this. The maximum amount of nitrate that can be present in water is 10 milligrams per liter. So what the class finds is that they find that their sample has 3/4 of this maximum value. So what's 3/4 of 10 milligrams per liter? Let's just write that down. So the maximum is 10 milligrams per liter. In their sample, they find 3/4 of this maximum concentration. So let's just multiply that. We can multiply that times 3/4, which is going to be equal to what? That is 7 1/2 milligrams per liter. So that is 7.5 milligrams per liter. The way I think about this, 3/4 of a hundred is 75. So 3/4 of 10 is going to be 7 1/2. You could have done it other ways. You could say 10 times three is 30. 30 divided by four is 7 1/2, and you keep your units. So this is the concentration that they find in their sample, 7.5 milligrams per liter. And they do this, they find this concentration in 15 liters of water. So the total number of milligrams they find, well, you take the liters of water, 15 liters, and then multiply that times the concentration. 7.5 milligrams per liter. Now, the units should work out, and they do indeed. You have a liter being divided by a liter, so those cancel out. Then you're left with 15 times 7.5 milligrams. So we just need to find out what 15 times 7.5 is, so let's do that. So if you have 7.5 times 15, five times five is 25, five times seven is 35 plus two is 37, and then one times 75 is 75. So let's see, five plus zero is five, seven plus five is 12, and then four plus seven is 11, and you have one digit behind the decimal point. They would expect to find 112.5 milligrams, and there we go.