here we're going to do unit conversions with multiple steps so where we've got to take a bunch of conversion factors and put them together in a row cancel a whole bunch of units to get to a final answer here we've got to find out how many seconds there are in 4 hours here's some pieces of information that tell us how the units relate to each other you might notice right away that there's no one relationship that lets us go directly from seconds to hours instead I have minutes and hours and seconds and minutes so this means that we've got to attack this problem in multiple steps here's our plan of attack we're starting with hours okay so we can go from hours based on this information to minutes okay and then after we have an answer that's in minutes we can take that and then we can convert to seconds let let's look at how we do this in what's going to be two different steps I'm going to start here with 4 hours okay 4 hours and I'm going multiply that by a conversion factor to get rid of hours so hours is here I'm going to want hours on the bottom 1 hour 60 Minutes is going to be up here on the top so now hours on the top hours on the bottom those cancel out I do four * 60 / 1 and I'm going to get 240 the units here are minutes now my answer's in minutes but I still got to go from minutes to seconds so that's what I'm going to use a second conversion factor here multiply the answer 240 minutes by second one of these I'm going to put one minute on the bottom I'm taking it from here and to get it into seconds I'm going to put 60 Seconds up here on the top so now minutes cancels minutes cancels and I'm finally left with seconds the method I'll do here is 240 * 60 ided 1 and that's going to give me 14,400 seconds and that's the final answer for this twostep problem this is one way the way I just did this is one way to solve a two-step problem but it's often easier to not worry about this intermediate answer the answer that I get halfway through and instead I can take these two conversion factors and I can just string them together right next to each other and then do the whole problem from start to finish kind of in one Fell Swoop let me show you how I'd rewrite this to put it all together into one I'd start with 4 hours just like I did before then I'd bring down this conversion factor 60 Minutes / 1 hour just to keep track of what's going on here the hours up here and the hours down there cancel out so now I'm left with minutes but instead of actually writing out this intermediate answer I'll just stick this conversion factor in here because now my units that are left they are minutes so I can take this second conversion factor which is going to get rid of minutes and put it right next to this here okay so now I have 60 seconds up here here and I have one minute down here and so the one minute down here is going to cross out the minutes that are up here remaining on this old conversion factor so this minutes on the top this has minutes on the bottom and now I'm left with seconds this can be really nice because now I can do all the math kind of in one step I can take this and plug it into my calculator as 4 * 60 / 1 * 60 / 1 and that's going to give me the answer that I got up here or if you have a scientific calculator with parentheses you can do it as four times the first conversion factor 60 divided 1 time the second conversion factor which is also 60 divided 1 and you'll get 14,400 both times so um let's do a couple more examples so that you get more comfortable with this here we're asked how many miles is 152,000 in the two pieces of information that I have here don't allow me to go directly from inches to miles instead I have inches and feet and then feet and Miles so feet is kind of going to be my intermediate Right feet is what I can get to from inches and then feet is where I can go or feet will let me go then to miles so the attack plan is going to be to start with inches and then convert inches to feet and then take feet and convert that to miles so starting this out with multiple conversion factors I'll have 152,000 in I want to convert inches to feet so I'll use a conversion factor based on this relationship so I want to get rid of inches so I will put 12 in from here on the bottom which means the other side of this uh equivalence here is going to be 1 foot and that's going to go on the top when I do this I like to cancel units along the way to make sure that I'm on the right track so that got rid of inches and now I'm left with feet okay now comes the second conversion factor I'm going to multiply this by something that will get rid of feet so I want feet here to be on the bottom so I'm going to do 5,280 ft and then the top will be the other half of this where I have one mile and now I have feet up here and feet down there and I'm left with units of Miles which is good because that's what I'm solving for so I know that I set this up correctly that what that's what can be so useful about this multiple conversion factor method is if all your units cancel and you're left with one unit that you need you know you set it up right so I always like doing this with a unit cancelling because I I know that I did it correctly so now we come to the math we'll do this in one step this times this divided by this time this divid by this I've written it out here or you can plug these in as conversion factors with parentheses if your calculator lets you do that whichever of these two methods you use to work through the math you're going to end up with an answer of 2.4 and the final units here are Miles we're going to do one more example and this is going to be a little bit trickier because it's going to be an example where we have to put three conversion factors together what is 350 tablespoons in liters and here are three pieces of information that we're going to need to go from tablespoons to liters let's look at how we're going to do it so we're starting with tablespoons so from tablespoons we can go to cups okay so tablespoons to cups that'll be our first step now now after we get cups we can go from cups here to gallons and after we're in gallons we can then go a to liters so these three units are part of what we call the English system and then the final here takes us into the metric system let's set this up with a conversion factor so we're starting with 350 uh tablespoons I'm going to multiply that by something that will get rid of tablespoons so I'm going to use this here so I've got 16 tablespoons on the bottom and one cup on the top I'm off to the right track because tablespoons cancel and I'm left with cups now I want to start with cups and get rid of it so I'll use another conversion factor that will put cups here on the bottom it'll be based on this equation it'll put cups on the bottom 16 cups and it'll put gallons on the top one gallon and now cups that's left over from this conversion factor cancels out cups in my new conversion factor cancels out now I'm left with gallons so now I'll go from gallons to liters and I'll need one more factor to do that I can use this relationship here I want one gallon to be on the bottom and then I'm going to want 3.785 L on the top gallons up here cancel out gallons down there cancel out and I'm left with liters liters is the unit that I'm looking for so I know that I set everything up correctly because everything else canceled out so this method gives you that peace of mind now for the math here's how look I should have made this uh made this a number in Black here anyway I do this times this divided by this times this divided by this times this divided by this and that's what I've written out there or as I've said before you can punch this in with a parentheses into a scientific calculator however you do it the answer that you're going to get is 5.2 lers so that's how to solve conversion factor problems where you need to string together a bunch of different conversion factors just remember to set it up so that your units cancel out and you're left with the final unit that you want and you'll know you've done it correctly it doesn't matter how many conversion factors you got to put together just just as long as you get rid of all the other units and keep the one that you're looking for you know you're set