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Anderson Video - Converting Units (Volume)

Professor Anderson
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 >> So let's say we want to convert units in volume. And let's take a specific example. Let's say we are looking at the density of water. Water is also known as dihydrogen oxide. Okay? What is the density of water? What do you guys know about water? What's the density of water? It is 1 gram per cubic centimeter. Okay. How much is that in SI units? Well, gram is not SI units, what is SI units? >> Kilogram. >> Kilogram. Centimeter is not SI units, what's SI units? >> Meters and we got a cube it. Okay, so let's see if we can do this. So, the density rho. This is the Greek letter, rho. It look s like a p that fell over. We've got 1 gram per cubic centimeter. All right, the easy one first. Let's get gram to kilograms. How many grams are in a kilogram? >> A thousand. >> A thousand. It's right there in the name, right? Kilo. So, we have 10 to the 3 grams in 1 kilogram. Piece of cake. How about centimeters to meters? >> A hundred. >> One hundred centimeters per meter. And is that the end of the story? No. Because what do we have to do? >> That's a cubit, right? We have to cube this quantity. We have to get rid of centimeters cubed, which means this centimeter has to be cubed. And so now look what happens. We're going to get rid of grams. We're going to get rid of centimeters cubed, and we are left with what? 1 times 1 -- 1 times 1 is 1 in the limit of small, 1's. Okay? And now we're going to take 100 and we're going to cube it. And we are dividing by 10 to the 3, and our units are kilogram per cubic meter. And so, what do we get? Well, 100 cubed is the same as 10 to the 2 cubed. And we have a 10 to the 3 in the bottom. If I take something like 10 to the 2 and I cube it, it becomes 10 to the 6th. And I divide by 10 to the 3 and I get 10 to the 3, which is 1,000 kilograms per cubic meter. 1,000 kilograms per cubic meter. Is that a lot of mass? Or is that a little mass? So, this is a good thing to remember. You will see this again and again on various physics problems. 1,000 kilograms per cubic meter for water. If it's salt water, it's a little bit more dense, okay? Fresh water at its sort of normal temperature and pressure, this is it. 1,000 kiloigrams per cubic meter. [ Music ]