hi everyone today we're going to learn how to do metric conversions so first we need to talk about what is a conversion factor so you use conversion factors all the time in real life without really realizing it like if you're told to go to a store and pick up um a dozen eggs you're asking for 12. so the conversion factor here is one dozen equals 12. because i could say do you have a dozen pencils that could mean 12 pencils we know that the word dozen means 12. so that acts as a conversion factor um here are is just like a little table of metric conversions that we are going to go through um time is another conversion factor that we use a lot in one minute there are 60 seconds and so forth i mean you could all make it all the way up to years and decades and we know how many years that is and so forth so we use conversion factors all the time without really realizing it but in science we use metric conversions that happen on this exponential scale exponents of 10. so we use something called dimensional analysis in order to apply our conversion factor the first thing we need to do is figure out what the conversion factor is going to be we're we're solving for this um here the 345 meters is equal to how many kilometers so first thing we need to do is figure out what our conversion factor is i'm gonna go back to one slide to this chart real quick there we go um there so we're gonna learn these but you can see that here kilo means a thousand or 10 cubed we're going to use milli a lot which is a thousandth or 10 to the negative three we're going to use centi a lot 10 to the negative 2 so we're going to do this all on another screen but just for now we can see that kilo means a thousand so if i have kilometers that means i have a thousand meter so 1000 meters is one kilometer the next step is to figure out the units basically so dimensional analysis means we're getting rid of new units and using our old units and using new units so we're switching between units these meter units in the problem is what we need to get rid of and the kilometers is what we need in order to move forward and get our answer right we're looking for kilometers so in order to cancel something in in math like if i had four i would divide it by itself in order to get one which is essentially canceling it that's what we're going to do so if i need to get rid of meters that means i need to divide by meters so i'm going to go ahead and write meters on the bottom and kilometers on the top and then use the numbers appropriately the thousand is with the meters the one is with the kilometers so here we have meters canceling and when we put this into our calculator we will get kilometers as our answer um so we would solve by doing 345 times one divided by a thousand to get our correct answer now in order to get to this point right where we figure out how to use our conversion factor again this is the conversion factor and we use it in dimensional analysis this conversion factor could really go either way right it just depends upon what units we needed if we were given kilometers and asked to find meters we would be putting kilometers on the bottom and meters on the top so whichever way we need it to work so that it cancels appropriately so now let's figure out what all those prefixes are and what they mean numerically so the prefix this is our there's giga there's mega there's kilo hecka deca is d a it's the only one that has two units our base unit goes here which i'll go over those in a second and then deci centi milli micro and nano um so the base units are like liters meters grams um you could have time in there so we we do say things like millisecond right so you could have seconds in there but these are the three that we're going to use the most and then what number do each of these stand for so we rarely use giga which is 10 to the ninth and mega which is ten to the six we very commonly use kilo which is a thousand heka which is a hundred and deco which is ten going the other way so that means our base unit is one knowing notice we're like counting down deci is 1 over 10 that's the same thing as saying 0.1 that's the same thing as saying 10 to the negative 1. but i think it's easier to understand as a fraction personally but if you want to to do these you can um millie's one over a thousand and then one over ten to the sixth and then one over ten to the ninth so it's the same numbers going both directions just these are in the numerator these are in the denominator because these are numbers smaller than one and these are numbers bigger than one but it's the same like power of 10 each direction so 10 to the 1 and then 10 to the 2 like going out both directions when you're using this in a dimensional analysis format the most important thing is just to know like how far away from zero are you or how far away from one are you sorry so if this is one how far away are you are you millie then you're a thousand you're three spots that's three zeros that's a thousand if you're kilo again that's a thousand it's important to know which of these are big units versus small units so remembering this sort of number line is will be useful so an example problem would be how many milliliters are there in 0.5 kiloliters of water so i'm asking for milliliters and given 0.5 kiloliters and i'm asking for milliliters i don't know how many so we always want to write our given first that's our first step so 0.5 kilo liters and then you have a couple options here so if you're memorizing like kilo is a thousand milli is a thousandth the easiest thing to do is put the unit we want to cancel on the bottom and then stop at that base unit in between so straight to liters then i can say well how many liters are in a kiloliter well i know kilo means a thousand so a thousand liters in one kiloliter and then you can continue on you put liters again on the bottom to cancel milliliters on the top and we know that there's a thousand milliliters in one liter so the one is always going to go sort of with the bigger unit the smaller unit is always going to have the number so again this is the biggest unit over here and this is the smallest on this side if you couldn't tell based on the numbers maybe that helps you remember it so again going across the number line and sort of memorizing this memorizing their order if if that helps you if memorizing them in order helps or memorizing what number they're associated with dusty's 10 70's 100 million thousand just having this in front of you as a reference is a good idea or having um this picture in front of you is also good as a reference because you will honestly use these so much that it will be second nature eventually so we're going to use a dimensional analysis with something you know and we'll work back to this situation where we're using um units you don't know so here it says a conversion factor can be created to convert american units to metric units and vice versa so it's asking us to change five pounds into grams and it gave us a conversion factor that one pound equals 454 grams so first step is writing our given which is five pounds and then our second step is deciding which one of these units pounds or grams goes on the bottom pounds goes on the bottom because we need that to cancel which means grams goes on the top and then they also get the appropriate number one pound for every 454 grams so taking five multiplying by 454 and dividing by one will get your answer um so here's another one again going from american units to metric units and vice versa so we're asking to go from meters to inches there is a conversion there that some of you may or may not know uh one inch is equal to 2.54 centimeters so we will need that conversion factor that's one we already know that we can apply and then we can use centimeters to meters in order to get to an equivalent here the centimeter to inches so we're actually starting with meters so we need to uh first put meters on the bottom to cancel and then we're going to put centimeters on the top right you can't go straight from meters to inches we need to stop at centimeters in the bottom so if you remember from the other slide one meter is equal to 100 centimeters remember centi was a hundred and so we're going to go ahead and put that into our uh dimensional analysis our final step then will be dividing by centimeters and converting that to inches so now we'll use this conversion factor up here one inch is 2.54 centimeters um i don't think i mentioned this uh when you cross this line you multiply when you cross this line you divide this is just sort of a shorthand that you're going to see a lot so keep that in mind when you're putting this into the calculator you'll do 3.5 times 100 divided by one times one divided by two point five four so every time you are below the line we're dividing and every time we're above the line we're multiplying if you guys want to take a second and pause this try it on your own and then come back that's probably a good idea but i'm going to go ahead and solve for you we're starting with 55 miles per hour and we want to get 10 meters per second so i'm going to start with my given miles per hour and i'm going to convert that into meters per second so miles is going to get converted to meters hours will get converted to seconds so i'm going to do the top first i'm going to start with miles uh so i need miles to go on the bottom to cancel and then i see here i have a miles to kilometer conversion so i'm going to go ahead and do that 1.61 kilometers to every one mile i don't want kilometers right i want meters so i'm going to put kilometers on the bottom and put meters on the top if you guys remember from the table a thousand meters equals one kilometer so i'm going to go ahead and insert that a thousand meters equals one kilometer so now i have meters on the top great meters these units cancel out kilometers kilometers miles miles so now i need to convert my hours here into seconds so i'm going to put hour on the top and then just because i'm given these here i'm going to go ahead and um work from hour to minute to second i know a lot of you might say well 3600 that's fine but i'm gonna just go ahead and do what we're doing so hour to minute so for every one hour i have 60 minutes and then i'm going to go from minute to second so for every one minute i have 60 seconds so again i can see my hour cancel with my hour right ones on the top ones on the bottom so they cancel i have my minute and my minute again ones on the top ones on the bottom so i cancel and i have meters per second which is my units meters per second so i've successfully converted it so when i put this into the calculator i'm going to do 55 times 1.61 i'm going to skip every place that says one because when you multiply or divide by one you get the same number so i'm just gonna skip those so times a thousand and then so i did those three i'm going to divide by 60 right there because i'm on the bottom so divide by 60 and here i'm on the bottom again so i'm going to hit divide again by 60 and equals to get my number here's another one if you want to pause it try this one yourself and then come back so an insurance travels at 15 millimeters in 12 minutes find his speed in inches per hour so i have 15 millimeters in 12 minutes and i need to change my millimeters into inches and my minutes into hours so let's do the top first so millimeters go on the bottom because i need to cancel and then i'm going to come up here and say is there anything that i can convert i'm going to inches so i want to use this one right because this one has inches in it but it has centimeters so that means i need to change milli to centi first so i'm just going to go back real quick to point something out to you guys um whoopsie it was right here so millie to centi is only one jump that's the difference between a hundred and a thousand so it's the difference between 10 to the second and 10 to the third so it's multiplying by 10 one extra time so going from milli to centi is a difference of a multiple of 10. so remember the smaller unit is gonna get the bigger number so that means for every one centimeter i have 10 millimeters so i'm going to go ahead and put that in and then i can convert my centimeters here to inches and using my conversion factor that's up here i'm going to do 2.54 centimeters to every one inch so that took care of my millimeters my centimeters and it left me with inches which is great i converted my millimeters to inches so now i need to do the other one minutes to hours so minutes is on the bottom down here so i'm going to put minutes on the top so that it cancels and then converting that to hours there are 60 minutes in one hour so minutes canceled and i'm left with hours in my denominator so i have inches per hour so now i can go ahead and enter it into my calculator once i've checked my dimensional analysis i checked it by canceling out my units and circling um the units i want into your calculator you'll do 15 divided by 12 divided by 10 because we're on the bottom right if it's on the bottom you hit divide if it's on the top you hit multiply so divide it again by 2.54 times oopsie times 60 not whatever that was going to be and you'll get your answer so here's a few more if you want to pause it and try it out before i get started um but here i go so we're converting 6.5 decimeters cubed so i'm going to cancel my decimeters cubed on the bottom and change it into centimeters cubed so the difference between deci and centi is a power of 10. the bigger unit which is dusty is going to get the smaller numbers so it's going to get the one and then centi is going to get 10. when your units are cubed you also need to cube the numbers so the one is going to get cubed and the three is going to get cubed so it's the difference between like a distance and a volume so if your if your unit is cubed make sure that you're cubing the number there's only one exception to that and we'll get to it in a little bit and so there you can see my decimeters cancel and i'm left with my centimeters which is what i want you could solve that by doing 6.5 times 10 to the third power next i'm going to do 6.5 liters into milliliters liters will go on the bottom milliliters will go on the top milli is 1 000 right so 1000 is the number we're working with there the smaller unit's going to get the bigger number milli is smaller than leader how did i know that you might be asking how did i know that when i look at my number line whoops when i look at my number nine line here's liter and here's milli right so liter is bigger than milliliter so again the smaller unit is going to get the bigger number um which is what i did there my liters cancel and i'm left with milliliters as my unit so again 6.5 times a thousand will give me the correct answer the same answer as the first part what a coincidence 6.5 liters now i can't go straight to centimeters cubed there's a conversion that you should know and that you guys should memorize one milliliter is equal to one centimeter cubed that's a conversion that you guys should know it's they're both volumes right milliliters of volume for liquid centimeter is a volume centimeters cubed is a volume for a solid um but one milliliter equals one centimeter cubed so we're going to use that conversion but in order to use it i have to first convert my liters to milliliters so liter goes on the bottom milliliter goes on the top we just did that conversion above and then i'm going to convert my one milliliter to one centimeter cubed here my whoops there we go here my liters cancel my milliliters cancel and i'm left with centimeter cubed so that's it as you start to work through your practice problems please let me know if you guys have any questions or if you need any more examples i'd be happy to make a few short videos just make sure you're posting to the appropriate discussion board and yeah have some fun