Converting units of mass
So I have two conversion scenarios right over here. I want to convert 3 kilograms into milligrams. And I want to convert 4 tons into ounces. So this is clearly in the metric system. And this right over here is in the US customary system. So I encourage you pause this video and try to do these conversions on your own. Well, to think about this one, we just have to think about what these prefixes mean. So I could rewrite this is 3 kilograms, and we're going to convert it into some amount of milligrams. And we've already seen that the prefix "kilo," this literally means 1,000. And the prefix "milli," means 1 over 1,000 or 1,000 of a gram. So let's just convert to grams first. Let's go from kilograms to grams. And then we can go from grams to milligrams. So we could say that 3 kilograms is going to be equal to 3 times 1,000 grams. So this is equal to 3,000. This is literally 3,000 grams. That's one way to interpret "kilo," so this gets us to 3,000 grams. Now, how to go from the grams to the milligrams? Well, we already said right over here that 1 milligram-- Let me write it here, 1 milligram is equal to 1 over 1,000 or 1,000 of a gram. But another way of thinking about this statement is that 1 gram is equal to 1,000 milligrams. So if we keep this in mind, we have 3,000 grams. Each of those are going to be equal to 1,000 milligrams. So this is equal to 3,000 grams. Each of those are equivalent to 1,000 milligrams, so times 1,000. And this is going to give us the number of milligrams. And what is this going to be? 1,000 thousands is a million, so 3,000 thousands is 3 million. This is going to get us 3 million milligrams. Another way to think about this multiplication, I've got 3 zeroes, here 3 zeroes here, so my final product should-- so 3 times 1 is 3, and then I should follow that with the 6 zeroes so I get 3 million milligrams. Now let's do the same thing over here. Let's convert this US customary ton right over here to ounces. What we'll do first is we'll go to pounds, and then from pounds we can go to ounces. And we know that 1 ton is equal to 2,000 pounds. So 4 tons are going to be equal to, well each of those are going to be 2,000 pounds. So it's going to be 4 times 2,000 pounds. Which is equal to 8,000 pounds. Make sure I have some space here. Now how many ounces are in each of those pounds? Well, we know that 1 pound, we know that 1 pound is equal to 16 ounces. So 8,000 pounds, so this over here-- so let me write this, 8,000 pounds. If each of those 8,000 have 16 ounces, or equivalent to 16 ounces, this is going to be 8,000 times 16 ounces. So what is 8,000 times 16? So this is going to be 8 times 16 is 80 plus 48 is 128. But we want to do 8,000 times, so it's going to be 128,000. So 4 tons are a lot of ounces.