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Dimensional Analysis Video

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August 27, 2013

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today we are going to learn how to convert units so for example if I have three 5 feet I can convert that to another units a centimeters and method that I'm teaching you here is dimensional analysis which is going to be required for the test I'm teaching you this method so you have to use this method it will be used in the future as well so it would be to your benefit to learn it this way okay so first of all when we are asked to find one unit and converted to another you are going to have know what the conversions are going to be  you should have been passed out you should have gone to paper the SI units and conversion table K that's this table right here which basically tells you what things are equal to one another hey this is where we actually get the conversion units so for example if you take a look at this example right here 1 m where is equal to 1.093 six yards that is a conversion factor we can show that as a fraction as I did the inches and the foot right here in your notes you can put the units of inches either at the top or at the bottom it really depends on what it is that you have and what you're trying to cancel out so I'll show you what that means in just a second just make sure you know that equivalence must have units that actually matches up to the particular numbers so 12 inches is equal to 1 foot or vice versa on the other side please don't make the mistake of switching the numbers around two units that are not correct for example I have here one one inch is equal to 12 feet it should say feet that sounds probably ridiculous you and it actually should because one in is a tiny tiny amount like it would say about that it's probably bigger on your screen but it supposed me about 2.54 centimeters but that's not equivalent to 12 ft which would be taller than a person now that's important because we're going to be working with units that may not be familiar to you so for example if I look back here at the conversion sheet we have some units called angst who's and picometers which you may not be familiar with and that's perfectly fine just make sure you know that these are conversion factors okay so what we're going to do is the factor label method to get rid of units that we don't want on top and then put down units that we do want sorry cancel can you set we don't want on the bottom and put units that we do one at the top some of these problems are going to be more than one step which is perfectly fine it shouldn't be too hard the cheetah doing these problems is actually relating the units to each other so let's go ahead and do an example I'm going to use one that deals with time since most of you are familiar with time already so let's try this one right here how many minutes are in 45.9 fortnights and there's a hit here it says one Fortnight is two weeks which is actually a conversion after because they are equal to one another so let me work out this problem with you if you take a look here hey we're going to start off with 45.9 fortnight's I'm going to write the time sign in and I'm going to draw a line  cake I'm going to put in a conversion factor now in here that's equal to one another but I want to get rid of the fortnight's on the I'm right here so I am going to relate fortnight's to something else that I know and in the problem it says that it's two weeks so I'm going to put in the units first fortnight's on the bar and weeks at the top and I always put in the numbers last because people make mistakes sometimes putting in their units right here and when they directions they sometimes leave the numbers in there and they will put down to fortnights as one week instead of the other way around which is 149 is to so always been in the units first and then the numbers afterwards so I'm going to put in a two right there and then one for thing there we go okay then I want you guys to Ashley Cross off the fortnight's right there and now what we have left is weeks now we're done yet the problem actually asked for the number of minutes so we need to keep going so we're going to write a x and draw mine again and we're going to put the units that we don't want on the bottom and right now for Knights is cancelled out so we actually have wheat so let's put weeks on the bottom right here and we can change weeks into another unit I don't know how many minutes there are in a week so I'm just going to go from two days and for every 1 week there are 7 days and I will continue to do this by changing days in 2 hours and their 24 days sorry 24 hours for every one day and I'm going to keep going cuz I have ours right now I need to get rid of the hours and change it into minutes which is the answer that I want this answer which is how we're going to answer the question and 1 hour there are 60 minutes so we are all done so the only thing we have to do now is to plug our numbers into the calculator so you can do this what two ways you can either multiply everything on the top so these numbers on the top and then / everything on the bottom to right now most of you guys are probably thinking it just says one on the bottom so I can just multiply everything on the top and you're right but later on when we do calculations that are a little bit more it may have numbers that are different so I want you to show you how you can do this in your calculator seen my calculator calculator 45.9 * 2 / 1 * 7 / 1 * 24 / 1 times 60 divided by 1 and I'm just going to punch that into my calculator and I'm going to get a number okay it turns out to be a really huge number I think it's 900 25000 some minutes for what I did was to get the three six six year was I looked at my original number where do with 45.9 that's actually 3 sig figs that's why I kept 360 The Final Answer in regular notation scientific notation deaths perfectly fine too if you wrote down 925000 with a common 3-0 that's fine alright now let's move on to the next problem which is not this one hold on one second let's try this one right here asking me for every 67.9 inches how many meters is that so again I'm going to start with my number with the unit 67.9 inches and I'm going to write down the times and then drop my mind and then I'm going to go back to the green to see if I can relate inches into meters so let's look back at the screen and all the conversion units are actually right in here and you'll see that there are no conversions of inches into meters there is a conversion factor that changes inches into centimeters you can either use that top one one or the third one but what I'm going to have you do right now is actually crossed off that second one because it's actually not as good as it's the third one here and I'll tell you what it's because of this word it says exactly so that's a much better conversion unit to use so I'm going to use that one right there one in his 2.54 CM like I said before I'm trying to change into meters and it doesn't they meters right here but I can't change my inches into centimeters which is related to meters so later on after I do that first step I can change centimeters into meters okay so let's look back now Kate on to the screen it says here that we have 90 sorry 67.9 inches hey we want to get rid of inches on the bottom and we're going to put in centimeters and I'm going to use that same conversion from our conversion sheet and it says for everyone in its 2.54 centimeters so make sure you put the numbers in the correct place so as of right now if you cross off the inches you'll see that I actually have centimeters so I have to get rid of centimeters and I know that centimeters is actually related to meters  if you can call back to 8th grade or 7th grade you probably learn that one m is actually 100 cm or you can write 10 to the negative second over one I personally prefer the other one so I'm going to show you the other one instead it was  centimeters on the bottom and then meters on the top for every one meter 100cm like this one better I think most of you guys probably know this conversion rather than this one right here either of them actually work when I come back I'll show you how to use these exponents right here I am done with the problem I canceled them and I get this number list the negative second in divided by 1 divided by 1 if you put the other number in there I think it was one over one hundred then you just the calculations as is * 1 in / on the bottom on this one meters so let's try another one that actually does not deal with distances but rather volume so here I have 4.9 0 0 1 gallon let's change the gallons into fluid ounces so let's take a look I'm sorry that this is moving so much my hands are tired and you right in here and you'll see that I actually do have gallons here I'm trying to relate gallons to fluid ounces right there but there's no fluid ounces here and 1 gallons equal to 4 quarts is also equal to 8 pints or 3.785 for but no fluid ounces if you take a look at the bottom one here it says that I have fluid ounces that can go to court so what I can do instead now is gallons into quarts and then quarts into fluid ounces so let's go ahead and proceed with this calculation so let's down our time sign again and then draw the line let's put gallons on the bottom and we said we can't change gallons into but we can change it into quarts first so looking back at your chart you'll see that for every one gallon there are go ahead and cancel out the gallons units and let's go on to the next one I have courts right now I want to get rid of it let's put it set volume and then we can change quarts to fluid ounces so we're going to look back at the Greensheet the conversion sheet and it says for every one quart there are three fluid ounces  now I just multiply everything on the top / everything on the bottom with five six days I would get 627.21 fluid oz and that is it for now you guys can work on the worksheet that Miss Spencer will pass out to you and hopefully I'll be back by the end of the pier to help you guys out with if you have any questions tomorrow we will be working on the lab that actually deals with these calculations help each other out work on this together see you later

Uploaded by Tina Yu-Wong.

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