expressing units okay so in this discussion we're going to learn the units that go with various quantities we're going to express them using their abbreviations and we're going to make new units by combining numerical prefixes with units so remember in a previous discussion we talked about a number indicating how much and the unit indicates the of what and so that of what is really important when communicating a quantity so let's say that you asked your friend how close you are to Lake Erie and your friend just says six you don't have complete information do you because you don't know whether that's six miles or six inches or six city blocks or anything so you know so basically you're kind of stuck okay the actual distance depends on what units that you use and so six miles would be obviously a lot different than six meters so these when we are expressing quantities we want to make sure that we combine a number with a unit and that's going to be all through this class numbers by themselves are relatively meaningless we need our unit okay so the SI which is the International System of Units there are seven fundamental units that are defined for various quantities and these are used all throughout science so it's really important to get familiar with these we're gonna focus on three fundamental units now and then we'll add some others laters so our three fundamental units right now have to do with length mass and time so length our fundamental unit is the meter for mass it's the kilogram notice that that is not grams that's kilograms and then for time it's going to be a second so here are just a few pictorial representations relating a meter to yards okay so you can see that a yard is you know not quite a whole meter so 0.9144 metres that's the conversion there for mass a kilogram is about 2.2 pounds and for time we all know that there are 60 seconds in a minute that's one that we all know we're already familiar now si also defines a series of numerical prefixes and those refer to multiples or fractions of a fundamental unit and it makes that unit more conveniently sized for a specific quantity so if we're talking about human hair which is really really really fine and we said it was 1.7 times 10 to the negative fifth meters that's really kind of strange I mean that's inconvenient it's a lot to write for a very very small number but if we use the micrometer prefix then we could say that it's 17 micrometers and 1 micrometer is 1 times 10 to the negative 6 meters so that makes it much much more you know easy to communicate our width of a human hair with micrometers as opposed to meters now we have multiplicative prefixes for SI units and 3 of them are larger than the fundamental unit and all of the rest of these are smaller than the fundamental unit okay so a kilo is a thousand of something Omega is a million and a Giga is a billion and and then you can just see you know as we go through here I Desa 10th centa 1/100 milli one one thousandth micrometer is we just talked about that that's a millionth nano is is a billionth and pecos are 10 to the negative 12 so very very small and so all like say all of these are much smaller and you're gonna see milli micro and even nano fairly often in chemistry because we deal with a lot of small things all right so what we're gonna do is we're going to combine that SI prefix with the unit itself and that's going to make a new unit essentially so so let's look at an example so one kilometer is 1,000 times a meter and that's going to be a thousand meters so if we have five kilometers then we're going to take five times a thousand because that's the definition of a kilo five times a thousand and we're going to get five thousand meters all right what about something that is smaller so a millisecond is one one thousandth of a second if we have 25 milliseconds then we have 25 thousandths of a second okay so you know a little bit bigger than just the one millisecond but still a very very small quantity a kilogram is a thousand grams and so if we have a hundred fifty kilograms then we're going to have to multiply a thousand times that 150 and we're going to get we're gonna get 150 thousand grams or 1.5 times ten to the fifth grams you can see in this case that the kilogram is a much better unit for that quantity all right so si also allows for derived units and we're all familiar with area so area is just defined as width times height and those are both lengths and they both have the fundamental unit of a meter and so if we multiply a meter times a meter we're gonna get square meters so that's what this m to the second power is okay and you can also have a prefix on your meters and still have the same thing so you can have centimeters squared you can have millimeters squared or kilometer squared okay so it's so really you can derive units with prefixes or or no prefixes either way is just fine volume is another derived unit and that's length times width times height okay and since the units for volume are meter then we're gonna have meters times meters times meters so a meter cubed so m to the third power is meters cubed we also call that cubic meters now if you take one one thousandth of a cubic meter which is this up here that's gonna be a leader okay and just compared to the court you can see that the leader is a little bit big so 0.94 liters is equal to one quart now cubic centimetres is actually related to milliliters and that's a really really handy thing to know especially when you're talking about density so another definition of a leader is 1/10 of a meter cubed okay and 1/10 of a meter is actually 10 centimeters if we cube it we're gonna get a thousand centimeters cubed and and if you're in the medical field or interested in that you've probably heard of cc's those are cubic centimeters and it turns out that one milliliter is equal to one cubic centimeter so keep that in mind that'll be very important and one liter is equal to one thousand milliliters so one thousand milliliters make up a leader and one of those milliliters is equal to one cc or one centimeter cubed so you can basically think of milliliters and centimeters cubed as interchangeable units that can be very very handy when you have leaders and you won't need to get two lengths for some reason now units can be multiplied together but they can also be divided and when we divide units then we're gonna get you know basically a vapor you know a situation so for instance if we're traveling at 1 meter for every second of time then our velocity is going to be one meter per second so that's 1 meter per which is that little backslash and then second so the word per implies division so velocity is dividing a distance quantity by a time quantity that's what we have up here meters per second other units for velocities they don't have to be meters per second they can be kilometers per hour they can be micrometers per nanosecond and we can see that other derived units will be expressed as fractions also that'll happen later on in the course so just in summary numbers tell you how much and units tell you of what and you were the unit's to make your number meaningful now we have a set of fundamental units and derived units from SI units and so those are the those are the correct units to use in science we also have a set of prefixes that represent multiples or fractions of units and again in chemistry you're mostly going to be dealing with the fractions of units although we do use kilograms and and a thousand milliliters to make up a leader very very often units can be multiplied and divided to generate new units for quantities and those would be our derived units