Units — Basic example

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 can that can be present in water is 10 milligrams 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 in the stream water is 3/4 of the maximum that is safe to drink how many milligrams of nitrates 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 when they tell us up here they tell us let me I'm doing this from car the maximum amount of nitrate that can be present in water is 10 milligrams per liter so what the 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 I can multiply that times 3/4 which is going to be equal to what that is 7 and 1/2 milligrams per liter so that is 7.5 milligrams per liter the way I think about this 3/4 of 100 is 75 so 3/4 of 10 is going to be 7 and a half you can done it other ways you can say 10 times 3 is 30 30 divided by 4 is 7 and 1/2 and you keep your units so this is a concentration that they find 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 unit should work out and they do indeed you have liter being divided by liter so the cancel out and you're left with 15 times 7.5 milligrams so we just need to figure out what 15 times 7.5 is so let's do that so if you have 7.5 times 15 5 times 5 is 25 5 times 7 is 35 plus 2 is 37 and then 1 times 75 is 75 so let's see 5 plus 0 is 5 7 plus 5 is 12 and then 4 plus 7 is 11 and you have one not one digit behind the decimal point so you would expect if they would they would expect to find 112 point five milligrams and there we go