converting units all right so our objective today is to be able to convert from one unit to another unit of the same type so let's start with an overall example for this process now this is a problem you can do in your head and that's one reason why we're using it so we all know that one yard is equal to three feet and it turns out that that's actually an equality and it can also be made into a conversion factor and so we can we can calculate this you know how many feet there are in three yards more formally if we use a conversion factor to do it now of course we we can all do it in our head so we know we're going to end up with nine feet but the interesting part is so here's our three yards and now we have three feet is equal to one yard and we're going to get an answer now what I want you to notice down here at the bottom is the three yards because yards is on the bottom in your conversion factor those units are going to cancel out so basically what you have here is three divided by one which is three times three feet so there's a unit that's still hanging around and so our final answer is going to be nine feet so we got rid of yards and we ended up with feet so this is basically the process we're going to discuss in this entire presentation now as I mentioned this is called an equality so you can do anything you want to this as long as you do it to both sides so for instance let's go ahead and divide both sides by two and we end up with one half yard is equal to one and a half feet that's still in equality we know that that's also still true now what if you divide both sides by a number and a unit okay so we have one yard is equal to three feet let's go ahead and multiply both sides by one yard and so one yard divided by one yard is equal to 1 3 feet divided by 1 yard that is our conversion factor that we just used so 3 yards divided by 1 yard gets rid of the yards multiplied by three feet gives us 9 feet now just one really important note conversion factors are considered exact so they are not counted when determining significant figures so I so in this case you know all of them have one but this would be one sig fig one sig fig but it doesn't matter what these numbers are they are in the Equality and they don't count towards significant figures because they are considered exact numbers okay so let's look at another example something a little less familiar so let's think about a millimeter now a millimeter is one one thousandth of a meter so we are gonna write down that definition right here one millimeter is one one thousandth of a meter now we can also write this where we have a thousand millimeters so lots of the little thing being equal to the big thing okay little thing equal to one divided by a big number okay there's another little thing or lots of little things equal to one big thing okay now let's go ahead and divide both sides by one meter so let's use the thousand millimeters equal to one meter we're gonna divide by one meter we're gonna end up with one on this side because one meter divided by one meter is one and we're gonna have one thousand millimeters over one meter now let's convert five meters into millimeters so we're going to use this conversion factor now notice this conversion factor has the unit we want to get rid of which is meters on the bottom and it has the unit that we want to convert into on the top that's going to be something a concept that you're going to be using a whole bunch when we talk about moles and mole ratios you're going to be using this so so definitely take some time to get familiar with this right now so five point five meters is gonna be canceled out by the one meter so five point five divided by one now we have a unitless number now we're going to multiply it by a thousand millimeters so now we have a unit back and we have five thousand five hundred millimeters if we write it in scientific notation it makes it really obvious that we have two significant figures in our answer just like we started with all right so let's do a different conversion this time we're going to go from millimeters to meters and we have the same two definitions and this time we're going to choose the one that that has that has thousand millimeters equal to one meter okay and we are going to divide by a thousand milliliters on millimeters on both sides okay and and this side is equal to one and here's our conversion factor there should be one more M there that should be millimeters not meters so one thousand millimeters divided by 1,000 millimeters is equal to one meter divided by a thousand millimeters okay and that's just saying that there's a thousand millimeters in one meter okay so let's use this as a conversion factor again so we have five thousand five hundred millimeters we're gonna divide it by a thousand now and that gets rid of our millimeter unit so five thousand five hundred divided by a thousand times one meter so now we get our unit back and we end up with 5.5 meters again notice we start off with two significant figures these are placeholder zeros we end up with two significant figures in our answer all right so how do we know which conversion factor to use that is the whole issue right there and again you're going to use this concept throughout this course so it's a really good thing to get down right now and basically the conversion factor you're going to use is going to depend on what unit you want to get rid of in your initial quantity okay so if you want to get rid of millimeters if you want to get rid of meters okay so same thing here this should be millimeters here so 1000 millimeters so if our original unit of our quantity is meters and we want to convert to millimeters then what we're going to do is choose this conversion factor because we're starting off with meters it's going to be in the numerator it's going to be cancelled out because this is in the denominator and then our millimeters is in the numerator and then we're going to end up with millimeters as our final answer so and so this basically is just stating so our original unit is assumed to be in the numerator to get rid of it we want the meter unit in the denominator so what we want to get rid of we want that in the denominator so it will cancel all right let's do a little bit more practice we're going to convert 35.9 kiloliters to liters so what's our equality we know kilo is a thousand so one kiloliter is a thousand liters we can revive we can write the conversion factor two ways so either one kiloliter over a thousand liters or a thousand liters over one kiloliter and now we're going to choose the conversion factor and calculate the answer so we're starting with kiloliters we want the conversion factor that has kiloliters on the bottom so it'll cancel out bye-bye bye-bye okay so a thirty five point nine divided by one which gives us thirty five point nine times a thousand is equal to looks like thirty five thousand nine hundred liters that's a lot of leaders and notice that we have three sig figs that we're starting with and we're going to end with three sig figs and these guys are both placeholder zeros all right another example let's go ahead and go from microliters to liters okay so we have one liter and that's a big thing and here's a whole bunch of small things so remember one liter is equal to one times 10 to the 6 microliters we can revoke we can write the conversion factor again two different ways one liter over one times 10 to the 6 microliters or the other way around now we want to convert from microliters to liters so we want to use the conversion factor that has microliters on the bottom so 60 7.08 microliters that gets rid of the Micra micro liter unit was where you end up with liter unit and we end up with six point seven zero eight times ten to the negative five liters as our answer and again notice our original quantity and our answer both have the same number of significant figures which is 4 so there's another sandwich zero that we have to count alright so just to summarize units can be converted to other units if we use the proper conversion factors we basically create those conversion factors from equalities that relate to different units we can have single step or multi step conversions so we only did single step in this presentation but you can do multi step also and unit conversion is a very powerful mathematical technique in chemistry you have to master it the other name for unit conversion is dimensional analysis so if you see that that's the same thing as unit conversion and then finally exact numbers do not affect the determination of sig figs so those those exact numbers in the Equality don't count when you're looking at sig figs