okay so let's do a little example with dimensional analysis we're going to convert 365.0 picometers to feet and we're given the following conversions to work with which one meter equals 39.4 inches and 12 inches equals one foot so how do we get started so what we want to do here is first find what we're going to convert so I like to start by writing that number down so we have 365 .0 picometers okay so what we're going to do now is think about it so we're not given the metric conversions we have to come up with those ourselves we have to memorize those and it turns out that one meter is equal to 1 times 10 to the 12 picometers okay so let's go ahead and use that conversion factor to get into meters and the reason why I'm going to do that is that our next conversion factor on our way to feet is 1 meter equals 39.4 inches so let's go ahead and get into meters okay so I'm going to put 1 times 10 to the 12 picometers on the bottom and one meter on the top now why do I put the picometers on the bottom well I need these guys to cancel out and so I'm using a conversion factor where the number of picometers here 1 times 10 to the 12th is equal to one meter so that's the same quantity but in different units all right so now all of our picometers are canceled out and we are now in meters so if I were to put this into the calculator I'd find out that it's 3.65 times 10 to the negative 10 meters now we're not finished yet of course because we want to go to feet so let's just underline that that's our goal so now we're in meters and now we're prepared to use this conversion factor one meter equals 39.4 inches so let's go ahead and use that conversion factor to get into inches so I'll set another one up here okay and I'm going to put one meter on the bottom because I need these meters to cancel out and I'm going to put 39.4 inches on the top so again just going back now we have we were in meters and now we have used a conversion factor where one meter is equal to 39.4 inches that's the same quantity the same length in two different units so now we're in inches and again if I were to go ahead and run this I'd 365.0 divided by 1 times 10 to the 12th multiplied by 39.4 I would end up with 1.438 times 10 to the negative 8 inches so that's where we are right now but again we are not finished so we still need to get to feet so we're ready to use our last conversion factor so we're currently in inches now we want to get to feet so let's do another bracket here okay we're going to set up another conversion factor now we're going to have 12 inches being equal to one foot all right so if we go back and cancel out our units inches on top inches on bottom so those are canceled out now we are in feet all right so now we want to do the math here and I'm going to write it out in gory detail just so that everybody knows what's going on so what we're going to do now that we have our dimensional analysis set up we want to multiply by anything on the top of a fraction okay so for instance 39.4 multiply by anything on top divide by anything on bottom okay so let's go ahead and do that so 365.0 divided by 1 times 10 to 12. okay then we're going to multiply it by 39.4 and finally divide by 12. and that's going to give us our answer so if we plug that into the calculator we're going to end up with 1.1984 times 10 to the negative 9 feet now we have to watch out for sig figs so how many do we have here let's go up and look at our initial quantity what we started with and we have 365.0 so remember because of that decimal point that oh that zero is significant so let's go ahead and count four there so now we're going to have to have 1.198 times 10 to negative 9 feet and that's our final answer