okay so now let's do an example of converting compound units so a compound unit is just a unit like this guy right here so we can see grams times centimeters cubed over seconds squared so it involves more than one type of unit all right so how do we start these basically i'm gonna do the same thing we have been doing and that is just write down what we're starting with and we're going to convert each one of these units individually so one at a time so it doesn't it's not as bad as it looks so let's write down 25.3 grams times centimeters cubed over seconds squared all right now as i said we want to convert one unit at a time so first i'm going to convert grams to kilograms because here's our goal and then centimeters cubed to meters cubed and finally seconds squared to hours squared so we'll go through that one step at a time so let's tackle the easy one first and that is the grams to kilograms so as before nothing's changed here we're going to convert grams to kilograms and so we have 1000 grams in one kilogram all right and i'm gonna go ahead and cross out grams so we are officially in kilograms right now so what we want to do now is convert these cubed and squared units and we have to keep one thing in mind when we're doing that so how many centimeters are there in one meter so we know that there are 100 centimeters in one meter so we have that memorized now what happens if we cube the centimeters so to the third power so i'm going to write that down here so we've cubed our centimeters what we need to remember is that we need to cube this number also and we're going to do the same thing on the other side so meters cubed and it's going to be 1 cubed now of course that's still just going to be 1. so that's why you may see a conversion factor that looks something like this 1 times 10 to the sixth centimeters cubed is equal to 1 meter cubed and so that kind of obscures what's actually going on but just remember whatever you do to the unit you have to do that to the number in front of it so if we want to convert from centimeters cubed to meters cubed then all we're going to do is apply what we did there so centimeters cubed is going to be on the bottom so we're going to have 100 cubed centimeters cubed okay so that's a little bit small maybe i can clean it up here a little bit make it a little bit bigger okay so centimeters cubed and we're gonna put one cubed meter cubed on the top and i'm just writing that one cubed so that it makes it really clear what we're doing but of course one to the third power is still just one all right so now let's go back and cancel out our centimeters so we have centimeters cubed on the bottom and that cancels out those centimeters cubed now we are in meters cubed now what do we do with time okay so we have second squared on the bottom and we want to go to hours squared so what we're going to do here we are going to remember in our brains we know that there are 60 seconds in one minute and there are 60 minutes in one hour now we notice that the seconds are squared and the hours are squared so we're going to do the same thing so for these two conversion factors we're going to have 60 squared seconds squared is equal to 1 squared minutes squared and of course that one squared is just one same thing with our minutes to hours so 60 squared minutes squared is equal to one squared hour squared all right so let's go ahead and put those in first let's convert our seconds to minutes so let's write so we have second squared on the bottom this is a little bit different so second squared on the bottom that means it has to go on the top in our conversion factor so 60 squared seconds squared and again let me just clean that up make it a little bit larger and we're going to have one squared minute squared all right let's cancel out our second squared make sure that we did that properly and we did now we're in minutes squared on the bottom so let's go ahead and convert minutes to hours minutes squared hours squared so we have 60 squared minutes squared over a 1 squared hour squared okay and so now we are ready to do our math all right so remember anything that is on the bottom or anywhere anything that's in the denominator we're going to divide this number by that anything that is in the numerator so on the top we're going to multiply so we're going to end up with 25.3 divided by 1000 divided by 100 cubed and then we're going to multiply by 60 squared which is 3600 and again multiply by 60 squared so when we put all of that in the calculator we are going to end up with 0.3 2 8 789 kilograms meters squared meters cubed sorry over hours squared all right so let's just go back and make sure that we've converted all of our units correctly so we have kilograms here we have meters cubed here and we have canceled out our minutes those guys are gone and so we end up with hours squared on the bottom the last thing we need to do is check our sig figs so let's take a look at our number the quantity that we started with 25.3 has three significant figures so we're going to end up with 0.328 kilograms meters cubed over hours squared as our final answer