so one of the most important things we need to pay attention to when it comes to reporting numbers that you get from calculations or measurements is to make sure that you use units units provide the context needed to understand what your number means and so this becomes super important especially in a class like this to get used to using the different units and when possible sometimes you will have to uh make a unit conversions so understanding these units is really fundamental and is something you really need to do well there is a i guess you could say a governing body called the international system of units or i believe it's french it's like uh system international d units or something like that s i stands for that sort of friends french abbreviation and in the sciences we tend to use the s i units and so therefore it's important that you know what they are so let's go through a few things uh length meter and by the way you'll note that these are all metric and as soon as you walk into a science laboratory you switch from the english system where we have pounds and and slugs and stuff like that and inches and yards to the metric system so you'll have to get very familiar with the metric system if you have not had much exposure to it well you will get a ton of it in this class so the the unit of length is the meter the unit of mass is the kilogram and uh unit of time the s i unit of time is the second and and you can see how you abbreviate these things and it's important that when you do use these units that you always use the appropriate abbreviation usually when we report a number we don't put spell out meters we would say 12 m now here's where the problem you'll see comes into play especially as you move on in chemistry or other areas of science sometimes these abbreviations are are actually used more than once on four unfortunately and for totally different things so in chem 111 you will not encounter double use of the little m by itself meter lowercase m but when you get to chem 112 we have this thing called molality which is also a little m so you kind of have to pay attention to the context of where that number is coming from and if you just saw 12 m well that could be confusing if you didn't have that context well in in the case of chem 111 m is gonna always mean meter we're not going to use that other situation that i talked about all right so then kelvin is a unit of temperature and we'll explore uh temperature units and take a look at them a little more detail uh ampere or the amp is uh electric current one that will we won't do much with amperes or candelas but we will use moles mole is like the chemist doesn't it represents uh an amount of a substance and we will dig into that much more deeply later on this semester now usually uh when i teach chem 111 and chem 112 or pretty much any chemistry i find that students have a pretty good grip on the the units of measurement in terms of the si units where they sometimes falter though is when using the appropriate uh prefixes so you will see that we have these prefixes uh tara now many of you because of the computer and and uh storage we have terra and giga and mega those and kilo kilobyte megabyte gigabyte terabyte well that tells us what that means so uh we're used to that a little bit but i don't know i mean to the sound of those but do you really know what these prefixes mean well in the case of a kilobyte using you know our computer uh that you're uh accustomed to you all have phones that have memory and stuff so a kilobyte is 1000 bytes a megabyte is 1 million bytes a gigabyte is 1 billion bytes and a terabyte is 1 trillion bytes and so you can do the same thing here and these are more uh i i would say in line with the kinds of examples you will encounter in this class deciliter i mean sorry kilometer megahertz giga years that's not one we'll probably use but that's an example or terawatts um what is a unit of power um so so you can see that for these uh for kilo mega giga tera that means that there's there are multiples of of a certain substance so if it's a kilometer you could have a megometer no megameter gigameter or terameter that's how you would say that but that then tells you how many meters you really have i think that a lot of times people use these in place of using scientific notation so you could say three megahertz is three times ten to the sixth hertz well instead of saying three times ten to the six hertz you could just say three megahertz that's kind of the typical reason for doing this and then you can get to fractions of the hole this is multiples of the of the hole if it's a meter you could do the same thing here for you could have a decimeter centimeter millimeter micrometer or micrometers and other you might hear nanometer people talk about nanoscale picometer femtometer so you need to really commit to memory and really get used to seeing these if you always have to look these up and say what does micro mean again oh 10 to the minus 6 of something or one millionth of of a substance is a micrometer uh or a micro that's what that means if you always have to look it up you're gonna get yourself you're gonna slow yourself down on the flip side it's better to look it up if uh you can't remember it well so looking going in this direction let's look at some of the examples so a deciliter is 1 10 or 1 times 10 to the minus 1 liters so it's one-tenth of a liter a centimeter seven centimeters would be uh seven times ten to the minus second meters or seven hundredths of a meter you have two millimoles uh this one is some something you will see a fair amount in this class a millimole is uh one one thousandth of a mole so 2 millimoles would be 2 times 10 to the minus 3 moles or 0.002 moles and and so you can work your way through this and see how uh what each of these means and how we would use them again this is important for you to understand so one way to really get to know your units and what the different units mean is occurs i should say when you are in a position to have to interconvert between the units sometimes that's necessary when you're doing certain calculations because you need your units to match uh sometimes and so that means you might have taken a measurement in a certain unit but then it turns out that you need it in a different unit in order to complete the calculation correctly so i'm going to show you a basic technique for doing unit conversions and this is very helpful because you can actually uh set this up in a certain way so that and i'll just say it and then i'll show you what i mean uh where the units can cancel each other out leaving you with the correct or desired unit that you are looking for so let's uh let's take a look at that so let's look at the first example here the first example it says to convert 78 let me just move this over a little bit 78 nanometers to kilometers and so the way i set these up excuse me the way i set these up is i begin by writing down what i'm starting with so in this case 78 nanometers and you'll see what the way i arrange this is i went ahead and i just put it over one i just do that as a way of setting this up and then way over on the side i have the equal sign and i know that i want my final units to be in kilometers okay so all i need to do now is think about when i when when i s start from 78 here i got 78 what are the conversion factors that i'm going to need to get all the way to my desired unit of kilometer well probably the easiest way to go about this is to maybe relate both nanometer and kilometer back to the meter and so one way to do that then is we know then we can set up another another group here where we have uh we want to convert this back to meters so for every 1 meter we know that there is nano means 1 times 10 to the minus 9th or 1 times 10 to the minus 9th meters or we could say that there's 1 times 10 to the 9th nanometers per meter the other option is i could have if i wanted to i could have put 1 times 10 to the minus 9 meters to 1 nanometer i tend to like to take the little one and say how many of that little one it takes to make a meter so a nanometer is one billionth of a meter or you could say there are 1 billion 1 times 10 to the 9th nanometers per meter that's the way i like to do it and then i go ahead and i now want to convert meters to kilometers so that's what i wrote here um i have 1 000 meters to one kilometer there's a thousand meters to one kilometer and then it's just a matter of making sure that i have the correct units once i do the math now we know that any number divided by itself is one well you can apply that same concept to units we have uh nanometers if you were to divide nanometers nanometers by nanometers you would get one so we can effectively say then that we can cancel those out because any number times one is equal to that number so what we're trying to do now is cancel out any units that show up in the denominator and numerator just like we showed here and when you can cancel them out when you can you see that one is being divided by the other and what are we left with kilometers so by making sure that we cancel out the units that we're dividing by um whatever is left over then represents the units of our conversion and so we are aiming for kilometers and now it's just a matter of plugging in these numbers into calculator and you should get if everything worked out right in your calculation you should get 7.8 times 10 to the minus 11 kilogram uh kilometers or kilometers and again i know i set this up right because i have my units cancelling each other out uh in the sense that we're dividing through like nanometers by nanometers or meters by meters and whenever you do that that's how you cancel out your units because any number divided by itself is one so if you let the unit kind of represent the number you can treat it the same way nanometers divided by nanometers is one and one times any number is that number so and if in effect we're cancelling out those units by converting them to one when you divide by itself and all that's left over then is the desired unit which is kilometers and so when you plug it in that's what you should get now you need to know how to use your uh scientific notation in your calculators i find a lot of students don't know how to do that and that has a lot to do with uh them having a more complex calculator like the ti you know whatever those are the with the 50 inch screen on them or whatever learn how to do that properly because so many times that's where people screw up when they're doing this kind of math they don't punch in their period their scientific notation correctly and they'll get the wrong number even though the setup looks correct now i want you to take a moment i want you to try to solve this one on your own and then i'll show you the solution start with kilograms 418 kilograms so that's what we want to start with and end up with milligrams that's what we want to end with and the rest is coming up with the appropriate um conversions i suggest you go through the gram kilogram one thousand grams milligram one one thousandth of a gram there's a thousand milligrams per gram and so use that information to see if you can do this conversion and then i'll share the solution with you so stop the video and try it on your own then turn the video back on and i will give you the solution okay welcome back hopefully you've gotten an answer for yourself i'm going to show you two alternative ways of to do this the way i do it is i again i start with my desired number i mean not my desired number my starting number so i have 418 kilograms and then i convert in this case it's helpful to go through the the main you know the the main unit which would be grams so i know that i for every kilogram i have 1000 grams and again my method i like i this is a personal preference thing but i always take the smaller unit gram or whatever the smaller unit is and say how many of that smaller unit there is in the main in the bigger unit so i know that there's a thousand grams in a kilogram and i just always do it this way it's my systematic method then i want to go from grams to milligrams and i know that there's a thousand milligrams in a gram okay remember i want to get my desired unit is a milligram so i can go through and i'm dividing kilogram by itself i'm dividing gram by itself so i can cancel those out that leaves me with my desired unit of milligram right there okay so then i have that all worked out and if i punch in the number or better said punch in the numbers into my calculator i get the following i get 4.18 times 10 to the eighth milligrams so in other words 418 um kilograms is um 4.18 times 10 to the eighth milligrams so that's 10 to the eighth let me make that sometimes my writing is is a little goofy there we go 10 to the eighth milligrams now i the alternative method i mentioned is instead of taking the small number and saying how many of that there is in the big number i have an alternative method and this way may make sense to you and it may be your preference you can do it but i would suggest you pick one of these approaches and always stick with that approach so i want i want to cancel out my kilograms so that part's the same so i know that for every one gram i have 0.001 kilograms so that's one way of writing that out and kilograms of course cancels out and i know that for every milligram oops for every milligram i have 0.00 grams and grams cancels out and i can now plug in the values and if i do what do i get well guess what i get this number 4.18 times 10 to the eighth milligrams nothing's changed so that's what you would get so you can see you can you can try this a couple of different ways but it really just takes practice and if you can master this unit canceling approach you will find that a lot of this math will work itself out you don't even have to think about it uh you can literally just cancel out units and get to the desired unit and it's all about knowing what your starting units are knowing what your desired ending units are and using the appropriate conversion factors and you always have a couple of choices with that conversion factor in this case i take a thousand grams per kilogram a thousand milligrams per gram and in the second scenario i said .001 kilograms per gram point zero zero one grams per milligram and so that's a pretty uh either one works for for some reason this way works best in my mind although i can do both ways obviously but this is the approach i usually take you'll know on my keys and stuff for tests or whatever that's what you will see all right let's move up to the next piece here now there's nothing earth-shattering about this it's more about units again and just kind of getting used to excuse me uh making unit conversions uh in different sort of contexts so in this case i have a cube and we want the volume and we know that the volume of the cube is going to be equal to length times width times height and since it's a cube if you know one of the lengths you know them all so we have 38 by 38 by 38 so if i go ahead i always write not only the numbers i'm working with but i also add the units right away some people like to add the units in the end and i i contend that that's a bad practice because in order to get the correct units you have to do the same kind of math on the units as you do on the numbers and that may sound like an odd thing but it's more like algebra where we use variables right that we can we can fit in so 38 cubed and the units will be meters cubed okay so in other words i can go ahead and i can write down what i get for that so 38 cubed is 54 872 cubic meters now i want to tell you something and we'll get to this eventually i'm going to keep all the digits but the truth is that would not be correct uh later i'll show you something called significant digits and that will teach us how to round this number so that we have appropriate number that reflects the level of precision that we have in our precision and accuracy that we have in our measurements but for now i'm just keeping all the digits even though technically that's not correct to do that but we will for now now the next thing is take the number of units uh that sorry convert this number of cubic meters into cubic centimeters and this is where it gets a little tricky okay because now the conversion factors are a little more uh involved okay and you'll see what i mean by that in a second so i'm going to start off just the same way we have before we have 54 870 2 cubic meters and again i usually systematically set up divide by one just because i i use this fraction method and so we need to convert meters to centimeters well i know that there's a hundred centimeters for every meter okay but we're not just talking about meters we're actually talking about cubic meters so in order to make this work probably the easiest way to see this is to say i know i have a hundred centimeters in a meter but we're cubing the meter so if i do that i could write it as a hundred centimeters cubed that way i'll go from cubic meters to cubic centimeters and what's really important when doing this is whatever that conversion factor is a hundred centimeters i need to also cube the 100 so it's it's not just you don't just put 100 centimeters cubed to meters cubed it's a hundred centimeters that whole thing cubed to meters cubed and when you do that you'll wind up with cubic centimeters and we'll be able to cancel out these units and so if we do this math we get the following so i get 5.487 times 10 to the 10th cubic centimeters and the key here is you have to cube the conversion factor as well as the units and so by doing that then you'll you'll get the the right kind of unit conversion so again unit conversion is important because sometimes you need your answer to be in a certain unit so that you can carry it forward in another calculation that requires a certain unit that's probably the most common reason why you would need to do unit conversion in real life okay here we go so the other some other volume units you know cubic meters cubic centimeters but of course the ones that we probably think about the most would be liters and milliliters things like that so it turns out that one cubic one cubic centimeter is a milliliter by definition so if you have a cubic centimeter that's one milliliter a cubic decimeter is one liter so we can think we can relate units of length to volume units that we're used to liters milliliters really straightforwardly when it comes to the metric system especially when keeping in mind that one cubic centimeter by definition is a milliliter so a thousand milliliters or a thousand cubic centimeters is equivalent to a liter another way to look at it is a decimal a decimeter cubed or a cubic decimeter is a liter and so now we can use all of put all of this together and we can do another set of unit conversions we want to this is kind of silly that would i can't think of a reason to do this kind of conversion however other than to get you practice doing the unit uh canceling methods and stuff like that so that sorry i'm having some technical difficulties oh there we go so again remember the the approach we're going to uh have 746 microliters that's our starting amount and we're going to convert it all the way to cube cubic kilometers like i said it's kind of a silly calculation however i want you to see if you can do this so go ahead pause the video see if you can come up with your own answer this is really important that you do this by the way it's uh it gives you some prac some guided practice and so you really need to do this you need to pause your video do the calculation and then you can always make the corrections once you see it that the one that i show you but it's really important that you try it first yourself so think of all the conversion factors that are involved and then how do we get to where we need to get to when it comes to our final desired unit okay go ahead pause the video give it a try alright so hopefully you pause the video and you're giving it you gave it a try and you came up with an answer now let me work it through and see if you've taken a similar approach so the first thing i would do is probably convert to [Music] uh something like leaders because leaders is something i can connect to i know for instance that a liter is a cubic decimeter but maybe just as helpful is knowing that a thousand cubic centimeters is a liter so if i can go through the leader it makes it for a very convenient uh conversion so that's what i'm going to do so i want microliters on the bottom because i know eventually i need to cancel that out so so i have microliters on the bottom and uh and then leaders on top but let me back up just a little bit if you remember from earlier a micro which is represented by the greek letter mu micro um leader means that there's a million there's a million 1 times 10 to the 6th microliters and so i can cancel out the microliters um for every leader all right so that gets us part way there um now we know that there is again the conversion factor i'm gonna use is i know that there's for there's a hundred sorry a thousand cubic centimeters for every liter i know that there's a thousand milliliters right for every liter and i know that a milliliter is equivalent to a cubic centimeter and so i can go ahead and cancel that out now my liters cancel out and i'm left with cubic centimeters now i have to go to cubic from cubic centimeters to cubic uh meters is probably my next best thing to do and i know that i have a hundred cubed cubic centimeters because remember i have to cube i know that there's a hundred centimeters in a meter but if i'm cubing the centimeters i have to cube that conversion factor so that's 100 cubed centimeters cubic centimeters for every cubic meter so then i can get rid of my cubic centimeters and i know that for every there's a thousand cubed cubic meters for every cubic kilometer and if i go ahead now i i can see that i can cancel out cubic meters and what am i left with my desired units cubic kilometer and now it's just a matter of doing the math on my calculator so i'm going to do that and when i do i get 7.46 times 10 to the minus 16th cubic kilometers did you get that same number if not find out where you may have done something incorrect my guess is it probably going to be uh in forgetting the cube one of those conversion factors okay let's move on so we talked about volume and we did some unit conversions let's talk about something else here's an intrinsic property i mentioned intrinsic properties earlier this is density and if you look in the boise state's general chemistry textbook it says that the density of a substance is the ratio of a mass of a sample to the volume of that sample and so usually typically you would find you know essentially density then is equal to mass divided by volume and and you can have many different units for density and it really depends on the substance for instance the density of a solid or a liquid is usually in grams per milliliter uh or sometimes you'll also see it grams per cubic centimeter which makes sense that you would see it in either way because remember a milliliter is nothing more than a cubic centimeter that would be for a liquid or a gas ah sorry liquid or a solid i said that wrong for a gas and we'll learn this when we go over the gas laws density is usually grams per liter and so that's because you'll find that gases are far less dense okay so just for fun let us do a practice problem so let's say i i have uh i'll call it substance x we don't even know what it is i'll just call it substance x and we want to know its density we want to know its density in units of grams per milliliter okay and what i let's say when i measured a certain volume of uh let's say i measured in one liter i'll i'll give it some extra digits there and one liter of substance x uh i'll just i think i want to just spell it out one liter of substance x okay has a mass of we'll say 8.50 kilograms what is its density okay so here's a case where we know that density is equal to mass divided by volume so we can say okay we got our mass is 8.50 kilograms divided by 1.00 liters now i want this in grams per milliliter so now i have to do some unit conversions all right so i want i want kilograms into grams well okay i know that one kilogram is equal to a thousand grams kilograms cancel out so i'm heading in the right direction and then uh let's see i know that i want to convert liters to milliliters and i need milliliters in the bottom so i'm going to cancel out my liters and i know that there's a thousand milliliters for every liter so what's kind of interesting is i can kind of do some quick math here we know that a thousand divided by a thousand is one so i can kind of cancel those out and so what units am i left with grams per milliliter and without even having to pull out the calculator i already know because the thousands cancel out that my answer is 8.50 grams per milliliter so learning to do these unit conversions is going to be a very important step for you i uh some people uh do something called train tracks it's a version of what i do here with all of my parentheses and stuff what they'll do is they'll set up they could do the same method and they use this technique called train tracks so what they do is they write their number you know five zero uh kilograms per one liter and then they put one train track in instead of using parentheses and then they put in their first unit conversion okay kilogram thousand grams and then they can cancel out their unit put in the next train track i've even heard people call this herringbone like fish bones same kind of idea and then a liter 1000 milliliters okay and so liters cancel out and then um i made i got a little too over zealous here with this i'll get rid of that and then you can go ahead and cancel those things out the thousands out and we're left with 8.50 gram per milliliter so sometimes when doing this some people like to do that i i think the only reason why i use this method is when i was in general chemistry that's how i learned it and i've done it that way ever since and i took general chemistry in college in 1986 so that's been a while ago okay so that's the end of this video