you okay let's go ahead and get started for today um as I mentioned on Friday today we're going to be talking about we're a little bit behind schedule but that's okay um mostly because a lot of these uh calculation things are a little bit um they're pivotal not just to this course but to any you know stem course that you're going to be going into in the future so I think it's a very good idea for us to invest time here so that you guys have a good understanding of how to do these kinds of problems and then uh our lives in the P will be a little easier hopefully all right for now as I as I was talking about we're going to be talking about some relatively simple conversions and we've seen a couple of them before uh easier one so let's say um here we were we were looking at you know the conversion of one day to 24 hours so it's if you were given 4.73 days you could convert that into hours using a conversion factor as seen here um similar uh situation so um let's say you can you know pretty much use this as a conversion factor let's let's actually start working on some problems right um so let's say we have we given the problem relatively simple one like this how many seconds seconds are in five days right so first off whenever you're given a problem like this step one is to just kind of figure out what the hell the question's even asking of you right and essentially here what we want is we want the total number of seconds in five days so in other words we need to go from unit of day over to unit of second right um so in other words we need to do a conversion which means we need conversion factors which we usually get as we were talking about last time from equivalency equival leny statements now um not all of these will always be given to you um that is to say sometimes you'll be expected to know some of these things off the top of your head um for instance these down here I don't think it's too much of an of an ask to you know to expect you guys to know that a day is 24 hours and 1 hour is 60 minutes and 1 minute is 60 seconds these are pretty common knowledge I would say but in the event of you know uh what's up fur long or something like that I would probably give you those kinds of conversion factors later on all right for now though we do know that one day is 24 hours 1 hour is 60 minutes and one minute is 60 seconds so let's go ahead take these equivalency statements and go ahead and make them into conversion factors um so how would I do a conversion factor here I just set it up as a simple fraction I say okay one day is 24 hours and likewise because these things are one in the same because I'm saying that they are equal to each other I can also flip this upside down and say that 24 hours is one day I don't think that's too much of a stretch for us to um worry about uh 1 hour 60 seconds or sorry minutes it's correct and then 60 minutes is in 1 hour H is just the there and then last but not least one minute is 60 seconds and then 60 seconds is one minute so for every equivalency uh statement that you can make you can always make two conversion factors the question is then which one do I use at any given time and so here are all the conversion factors that we just made and really at this point now that we have our conversion factors we're going to go ahead we're going to start with where we know so with what we know so what we start with is five days five days and we eventually want to try to figure out how what this is in seconds right what is X okay in order to do this the best way is really what I call just following your units right um remember that we are trying to do dimensional analysis and really what we're trying to do is we're trying to get units to cancel get this to cancel until we end up with the units that we want in this case seconds right so okay um what is it how do you get a unit to cancel divide it by the same unit right so if I do that uh one thing I do want to mention real quick is that um blue whenever you're given a value just like five days like this mathematically speaking you're allowed to just put it over one anything divided by one is itself so you can always just take a regular number like that and turn it into a fraction by just putting it over one you don't need to do this this is optional but it may help you visualize setting things up a little bit more easily why because now we're going to want to convert days into something a little bit more useful um do we have a way here to directly go from days to seconds do is that one of our options for our conversion factors no not immediately so we're just going to take it one step at a time and see if maybe after doing a couple of these we can actually make it over to seconds um the ones that I see that have to do with days are this guy and this guy here but remember we are trying to divide this I uh divide it by something that has to do with days or in other words I want for my next step to have days in the denominator uh which one of these two gets me there the second one right so I'm going to label them one two 3 four five six and as you guys mentioned we're going to be wanting to use number two right there because two gets us those dat in the denominator all right so it's 24 hours in one day and oh look a cancels day excellent um but are we in the unit that we want not yet so with these conversions you're not always going to get a simple one-step conversion oftentimes you're going to have to chain a couple of these um uh conversion factors together together to get to where you want to go all right so fine um we're in hours now is there a way for me to go directly from hours to seconds not quite but we might be able to take one step further what do you think is the next thing I want to install here 0 minutes per hour why is that that's very good hours perfect right right now we're in units of hour which means I need to have hour down here some somewh somewhere and the only one that does that number four all right so that's going to go right there we're going to say 60 Minute in one hour hour cancels hour very good and now we're units of minutes is that what we want still no not quite yet looks like we need one more is there a way for me to finally get to the unit that I want absolutely there is we're going to take it to Orange we're going to say okay well I need minutes because that's what I'm in right now I need those on in my denominator and the one that gets me with minutes in my denominator is 60 seconds and one M that's a minute and one minute and oh look okay minutes cancels minutes what unit am I in now is that what I want absolutely that's what I want okay so now we say um 5 days * 24 * 60 * 60 so that'll be 5 * 24 * 60 * 60 divided by 1 * 1 * 1 * 1 and then last well this unit got canceled with that one so we don't got to worry about it that one got canceled with this one don't worry that one got canceled with that one don't worry about it our final unit is going to be seconds and let's go ahead get our calculator 5 * 24 * 60 * 60 gets us to 4320 seconds good all right um let's not worry too much about Sig bigs for this one because that could open up a c of wordss that I'm not quite ready to talk about yet but we'll get there in a little bit so don't worry about Sig bigs for this but okay um actually no let's do worry about Sy things because this actually brings me to a good point let's say that in actuality this here was a measurement and I took a stopwatch and I measured and based on my stopwatch I found that my measurement was 5.0 days uh how many sigfigs are here two uh remember tailing zero behind both a sigic and a decimal point that one's going to be significant so this value here carries two significant figures um the these are defined by humans defined defined and defined we have said okay uh in 24 hours or sorry in one day there is exactly 24 hours in one hour there are exactly 60 Minutes in one minute there are exactly 60 seconds so what do we say about these sig figs for these members infinite sigfigs because we have defined them we say that it is 60.0 minutes in one hour so all of these infinite Sig pigs and what's the rule for multiplication when it comes to sigfigs pick the lowest number of sigfigs right so in that case we're Li limited to how many sigfigs two two sigfigs so that means that this number here needs to go to two sigfigs um how many sig does it have currently has three right we have um going this one so that's one two three and then these are without any decimal point there they are ambiguous and they do not count either way we've got a bit of an issue because currently our measurement has more sigfigs than what we need and what we're able to report so um how how could I what any guesses on how I might want to handle this situation huh move the decimal back one space move the decimal back once so if if you're from the zero you move it back once move back four or five thing move it back one two on one two three four yeah so you're saying I should write this as 43.2 seconds you're getting there though you are burning hot scientific notation right and one move it over one more whoops trip on the mouse because it needs to be between all right first scientific notation what do you mean by that like it can't be 43.2 because you can still go and move the decimal one further right right so by 10 to the power of right so I think I kind of see what you're saying so this is technically not standard scientific notation as as you were mentioning usually we're going to want to write scientific notation as 4.32 time 10 to the something right so let's go ahead get rid of these and the question is what is the value that goes here and as you guys were saying we just got to count how many times we move that decimal point over right so it's 1 2 3 four five 10 is it plus five or minus five plus five right because we are taking a relatively big number making it look a little bit smaller that means that we need to have a positive value there positive in order to once we go backwards one two 3 4 five we can restore any missing digits that we took away but okay so 4.32 * 10 the 5 um this still has too many sigfigs though right so what do I do now just round that sucker right so all I have to do is be like okay three CES two does it round up or does it St the same stay the same so my final final answer 4.3 * 10 to 5th seconds this is basically what happens what you need to do if your answer the answer that you calculate has too many sig pigs and is also too big usually you just pop it into scientific notation and then round to the appropriate number of signific digits okay yes did I let's see did I screw that up one two three four five so I move the decimal point over to the left five times yeah it's just how many times you you move that good you have a question yeah um can you explain again why it's uh right uh it's because it it's a little bit they aren't measurements that is to say they are something that we as as a collective human have uh kind of decided for ourselves um basically it's us saying that there are exactly 60 minutes in an hour and that means 60.0 it's not you know there's not a little bit of wiggle room in there it is 60 minutes exactly um for instance this is where things can get a little bit tricky in terms of looking at scientific sorry at significant figures um how many tables is this one would you say that there's room for error in that measurement is there 1.1 table no 1.01 table 1.01 table no it's 1.0 oh because we know I'm looking at it right now it's a table and it's right in front of me right and there's one of them and it's exactly one it's kind of the same idea here where I'm saying yeah there's 60 minutes in an hour and there are exactly 60 so that's going to that's 60.0 blah blah blah blah blah so therefore I would argue I would say that that has infinite number of six does that make a little bit more sense okay yes so it's just like because we've made up both minutes and seconds and we said so like we said that 60 seconds makes one minute yeah we know for a fact but it's just 60.0 because we said so because we said so and it's the same idea with this stuff over here right uh yes I I do I am able to measure individual meters and stuff like that but when it comes to uh jumping in between a kilometer and a meter well us as humans and as scientists we have defined this we said oh yeah to make our lives a little easier 1,000 MERS exactly so 1,000. meters exactly is 1 kilometer and 1 kilometer 1.0 exactly is a 1,000 M these are just things that we have defined for ourselves they're not always going to be this nice most things that you convert are not going to be this nice but just keep in mind that if something kind of sounds like a definition good chance it's going to carry infinite signs okay question yeah ah so those two sigfigs uh came as a result of me setting up the problem and they came from right here essentially all I did was I said okay instead of just giving you five days I'm going to pretend like I I took a timer and I measured five days and my timer happened to give me 5.0 days so this is a measurement measurements always have a limited number of Si things that's a good point so measurements measure Ms always that's not how you spell always always carry a specific number of signs and in this case if I'm treating this as a measurement then that guy there 5.0 only carries two signicant questions or other I get you oh good not necessarily no because it depends on your conversion factors too in this case our conversion factors were all considered to have infinite sigfigs and the rule for multiplication and division is lowest number of Sig bigs if if say we were in in another world and maybe that value there only had one Sig fig then our final answer would be limited to one Sig fig even though our initial measurement had two okay so it depends it really does depend I saw another question yes oh so it was two Sig bigs but what if we just started what if it was just five it would only be one SigFig it would be one SigFig yes yes our result wasn't 432,000 and let's say those zeros became like other numbers like 125 how would we condense that into two significant figures cool I like that question so let's say that instead we had 4 3 2 1 51 seconds let's say that that was our answer right so the question is how do I get this into two Sig bigs and honestly the the answer is pretty pretty much the same what you do pop your decimal point down and you say okay I'm going to go ahead and put this into scientific notation 1 2 3 4 5 so 4. 32151 * 10 to the 5th so just the same process and then from there you say Okay I want two sigfigs these are the two that I want three CES two and it still just rounds down 4.3 times same process even if it's zeros or numbers that are right there good question back there I just want to ask uh I I don't know if I comprehended it but uh why why is 526 F to 5.0 if it's just a normal five I'm sorry one more time like um why is what why do we add the point0 for five days oh um that was that was me adding it for the sake of doing a sign problem oh okay yeah that that's all that was okay it's not it's not that 5 days inherently has two s fixs for some mysterious reason I just put that in there for the sake of argument for this problem okay yeah other questions these are great I love it good okay let's us oh whoops I forgot about those oh well okay um so let's go ahead and instead work on on some practice problems actually I might want to go ahead this looking a little bit crowded so let's go to photoshop roll with that all right all right so let's look at the first one here Alex can grade 5.5 lab reports every hour right so 5.5 lab reports every hour he's got 52 students although this case I actually happen to have more so this is an important uh interesting tidbit and each student has turned into a report so each one of you did your report uh you guys are good students right how long how much time how long much time what how much time does he need to grade so in other words um I'm going to go probably from um number of lab reports looks like lab reports two time right okay that doesn't seem too bad um real quick let's just go ahead is there an equivalency statement that I can make from this do you reckon or a conversion factor this is just a conversion you go the 5.5 Labs or one hour and I can also say 1 hour 5.5 laps okay and then the last bit of information that I have I need is 52 students or also 52 Labs okay so let's go ahead we'll transfer that over to our workspace 52 labs and then 5.5 uh labs for one hour or 1 hour 5.5 labs and ultimately what I want to know is I need this in terms of some time unit right if I specified I wanted it in hours or days or or you know months or something you would um you would probably specify it there but for now we'll take you know seconds or minutes or hours or days or weeks or months just whatever unit is in time will work for me unless I specify other ones but okay so we have 5 two labs and that's over one and for here let's go ahead and think to ourselves okay I have units that are in Labs um which one of these two uh conversion factors do I want to chug in so number two why uh because you're canceling out labs to get that bingo so we have Labs up here which means I want to be seeing Labs down there so that they can't 5.5 in one hour so Labs cancel labs and then what do we see we see Okay calculator where are you there the calculator I already got it for me I got 94 five 94 five4 five okay now I now I hear what you guys 94 five four five four five uh hours so um question is are our units good at least yeah because I have you have given me an answer that is in time uh if I said I wanted it in minutes then I'd have to convert hours to minutes but I was non-specific so don't even worry about it you gave me an answer in time good second question is then are we is this a good final answer no because again always Sig pigs um question question question question you know how I pointed at this table and I said I counted the number of tables and we have exactly one student one table right right if I had a stack of labs and I counted them one lab two lab three lab four lab five lab 52 Labs how many sick figs do you reckon that would that would carry I hear two and I hear Infinity what's the argument for two there's only 52 Labs but is there really such a thing as like half a lab that I grade no right and it's not 52.1 Labs it's not 49.9 Labs it's 50 it's exactly 52 Labs right so if we're working with something that we know exactly 52.0 Labs well this here in theory should carry infinite Sig BS right and this one's an approximation I just kind of gave it to you but based on the numbers here how many sig pigs two two Sig pigs uh put it this way another couple of examples right um if I were to count every single person in this room and let's say uh I counted and there were 71 students in the room how many sigfigs would that measurement cuz I measurement measure it how many sigfigs would it carry infinite right is there such a thing as half a person no I mean I'm halfway dead but I mean I still count as a whole person hopefully um is there such a thing as 0.1 person no right a person is a person regardless of if they're missing a hand or anything like that so if I count 72 or 71 students 71.0 students that is um that's a measurement that actually does carry infinite Sick Things what about um a dozen eggs right so I go to the supermarket I buy a carton of eggs I open it up none of them are cracked and I count them one two three four 5 6 7 8 9 10 11 12 12 eggs in my dozen how many sigfigs in that measurement it's infinite because I know that there are exactly 12 eggs um and there uh there's no such thing as 0.1 of an egg there's no such thing as as 9/8 of an egg it's they're all there they are whole things and I can count them and know them exactly all right so in this case uh 52 would be considered to have infinite sig figs 5.5 would carry two sick figs which means our final answer has how many sick figs two one two all right so four C is five what does it do round up Final Answer is 9.5 hours or in other words it would take 9.5 hours to grade 5 okay some little subtleties with these six big uh calculations uh practice is the key here okay questions before we do another yes um in the future when it's like infinite amount of State FS is this the kind of answer you'd be looking for the previous practice where you had to put it in scientific notation or it's already so it depends um that and it's honestly a great question so here remember that scientific notation is usually in the form of a point B C uh a point B C d e * 10 to the something right and here well this is our a point B so we're already kind of there there is just sort of a hidden 10 to the 0o that's right there and why is there a hidden 10 to the 0o because 10 of the 0o is one anything times one is itself so this is already technically in scientific notation but let's run with this for a bit let's say that in another another reality perhaps we had uh our answer was actually 945 45.5 uh 4 five hours right and if I wanted to get this into two significant digits well then at that point that's when I go back to that previous trick and I say okay there's my decimal point I'm going to move it over 1 2 3 4 to get me to 9 454545 * 10 to the what four very good hours right and then I say okay well now I need this in two significant digits one two four looks at five and rounds up 9.5 * 10 4 hours that's how you would take a number like this and round it to two signific scientific notation is important got it yes cool other questions all right let's keep going keep going keep it going um we'll do slip and Jimmy because that one actually has a good number of steps to work so slip and Jimmy won his latest lawsuit and was awarded uh 8,229 in compensatory damages so that's a good piece of nothing about uh he eats only Big Mac Meals and needs two every day so two Big Mac Meals every day and each meal costs $15.78 how long so time how long can how many days or minutes or hours or months or whatever can he eat so let's let's dissect this a little bit we're starting out uh one piece of information is that he's got a lot of money 118 229 right and based on some of this information looks like it's going to be one Big Mac meal I'm going to abbreviate this as bmm um sorry it's actually two Big Max in one day or one day he will eat to Big Max all right and then each meal so one Big Mac meal is 1578 or he can pay 1578 for a Big Mac so question is then I need to somehow weave all of these things together to get me from money to time because time is indeed money maybe uh let's just okay so let's go ahead rewrite some of this I need a bigger art board so we're just going to go ahead go away he your nonsense me give me more there we go and then back to oh away okay so one 18229 doll and we need to get this into units of time right and I'll also rewrite our conversion factors that we got from our problem one day two Big Mac Meals and then one Big Mac meal is overpriced eight okay here we go this is what we know so let's go ahead let's take a look at where we start 11 18229 and currently although you usually units go here uh we're talking about money so really the only unit that we're working with is the dollar and what can I do with this particular dollar how so main idea is that again we're trying to get to units of time which means that down here in my denominator what unit do I want to see I want to see dollars right um which one of these is the only one that puts dollars in the denominator so one Big Mac meal is $15.78 cents and oh look money cancels money good all right so now we're in units of Big Mac Meals uh not really time though right so how can is there a way for me to go from Big Mac Meals to units of time right this one here we see that he eats every one day two Big Mac Meals and also Big Mac Meals is in the denominator which is exactly where we wanted so that it cancels out with the one that we got there let's go ahead put that in one day two Big Mac Meals bmm cancel good and now we're left in units of day are we okay with this oh why do I have change Towers aren't you aren't you trying to get time after time time I was thinking if you divide it by the 24 hour to put in the hour but I guess the day works too I was thinking a different way that's why so if if we wanted to take it to days or sorry to hours then you would be correct let's say I wanted I specified that I wanted hours right okay if I'm going to be that specific then at that point you would be absolutely correct you would say yeah I'm not quite done yet I would need to know that um 24 hours are in one day all right uh you could stop here or you could carry it on so long as the answer is correct at the end of the day and you're giving me a value of time and that's all I asked for sure why not okay so days cancel days we'll leave it in hours just for Shi and Giggles because why not um and now we are in some sort of appropriate unit before we do our calculations let's go ahead and think about s bigs first off we're doing multiplication so um what's the rule least number of Sig pigs very good how many sig pigs in 118 229 six sig figs how many in uh 1578 and then um here we're saying that he eats exactly two of these meals he doesn't eat 2.1 of them he doesn't eat 1.9 of them um so how many sigfigs do you reckon are here infinite sigfigs because it he eats exactly two of these meals that's all he eats he doesn't eat any more doesn't eat any less yes tast we know exactly that's how much money a good point yeah you know what so the question is he he can he can take all of these dollars plop them on the table and know exactly how many he has why isn't it infinite Sig pigs and you know what after four times of giving this lecture that's the first time someone's brought this up great and you know what I tend to agree I think you're actually correct on this good catch I would actually feel the same and say that this is infinite Sig big because he knows exactly how many dollars he's got in his bank account and so does Bank of America right so based on that logic yeah I'm tempted to to agree and say infinite sigfigs there apologies uh lots of questions from that one so let's move left to right yes um this one is have just like make sure Vigilant yeah so be fair uh these examples I guess I planned them a little bit sillier than I thought I didn't really think about them all the way through um I was I was kind of treating this as a bit of a measurement I wasn't really thinking it's you know 78.0 cents um so really I was just trying to trying to take it easy and and really only roll with it for four SI bics although technically you know it's exactly one Big Mac meal for exactly $15.78 so technically it would be infinite it's to um for exams we're not going this silly and and I it will be much much more obvious I'm not going to be messing with dollars I promise you that now okay not messing with money in the future but uh for now let's just take it as 46s for for the argum but I I see where you're coming from okay uh yes yeah because like with dollars it's any measurement that you're given in dollars can technically be an exact be exact right you can break it down into pennies if you really want it yeah and all of that would be exact so you guys are absolutely right and that's actually something I'd never really considered when I was formulating or explaining these problems so good on you for poking holes through my argument glad to see you all at paying attention for now let's roll with four but I agree really it should probably be infinite and infinite and infinite and we wouldn't really be worrying about sig figs for this for now though let's just let's pretend that we're rolling with foring things okay this is pretend absolutely clear even on the recordings okay so then based off of this we say okay we're in the appropriate units and we've accounted we're going to we're going to roll with four significant figures let's see what we end up with let's see 11 18 229 divided 15.78% 118 229 1578 by 2 * 24 gets us to 8997 89 907 something hours but of course we're going to put this into four Sig bigs one two 3 four and easiest way to go about doing that probably scientific notation 2 three four this is 8.99 uh 0 C7 what happens rounds up 991 * 10^ the 1 2 3 4 10 to the 4 hours four safe figs and it's given in a unit of time all right uh aside from the you know botched cic arguments there question my years you put it in uh I uh if you put it in years I would feel compelled to accept any time measurement if I was non-specific so if if I told you you know um you know give just give me a time and he decided to put it in decades sure you could do that and I couldn't really argue argue with you that's an appropriate time measurement um but if you're on an exam and you're just like oh well this one gives me the the unit in time and that's all I care about then that's probably best for you not to make your life easier yes problem two every single day is that our unit of measurement flat so like like are you're measuring time right asking how aspect of day right so we're trying to find out how many days he can eat for I days it could be how many days he can eat for how many hours he can eat for just basic the question really is just like uh once he has this money how long can he survive off of Big Mac Meals it could be hours it could be days it could be seconds and microc seconds doesn't really matter uh so long as an answer that makes sense to me okay yes um I will probably give always give you some spe like some measurement or something to convert that will limit your number of signs generally that's just how I work okay cool let's see uh what time is it okay maybe I'll do I'll do one quick um it will work with big Sally here she can walk oh this is weird uh we'll just say that this is SSP walk from there to there in 7.3 minutes um timed herself she walks at 14 m/ second what's the distance between the two rooms so here 7.3 minutes and we want to go to a distance measurement right and what we know just real fast it's um 14 m/ second is what she can walk at so 14 m/ second and if we want to go from 7.3 minutes well question for you can I instantly use this conversion factor no because we're in seconds here and we're in minutes there so what I need to do first is I need to convert this to seconds and I say okay there's uh 60 seconds in one minute now the minute cancels the minute and now I can say oh yeah 14 meters or one second oh yeah second cancel seconds If I multiply these things together I should get get an answer this will be two Sig bigs this is infinite because we defined it and then this is also I think a measurement so two Sig bigs Final Answer whatever it is should be in two sig figs let's go ahead do that real quick 7.3 7.3 * 14 time 60 I do that correctly oh that ends up being 6132 6132 M uh but this is 46 big so this will be 6.1 uh whoops 6.1 * 10 3 m as the final answer so she can actually walk pretty darn fast right um I recommend that you guys work on some of these problems uh go through the problems that are on the rest of the slides as well if you have questions by all please let me know otherwise I think next time we're we're jumping on to chapter two