hello there I just wanted to talk to you a little bit about measurements just in time for doing our first lab that has a lot of measurement work inside of it so what I want you to do is just look at this ruler up here there's a shaded box right above the ruler right here well all I want you to do is I want you to measure the length of that box and go ahead and write down your measurements so this is a good time to pause the video not using any fancy thing to make you pause but just pause the video write down your answer what is our measurement for that box okay did you actually do it did you actually pause the video and write it down come on please go back write it down actually get a measurement for it because it'll help you understand where either you went wrong or where you went right so that we can move forward all right so it turns out most people who look at this will write down somewhere around six and a half of the write down maybe six point six sometimes people will write down six point oh five when they count five over or they'll count six point zero six when they count six over none of these are correct for a few reasons one none of them have units first we have to figure out what are the units on this device the next is it turns out that none of them are correct numerically and we'll see why that is in just a moment but the first thing we have to do is zoom in a little bit on our ruler to see what is correct so the first thing works the first thing we're going to look at is the units down here this thing says millimeters now of course we're on screen so I can make up whatever I want but let's say this was just a regular sized ruler and had these markings that were about yay far apart that were marked one two three four is that a millimeter well in order to know that you have to know what a millimeter is and a millimeter is about the height of an ant okay so chances are those one two three four is marked about that hang big are not the size of an ant because that would be an awfully large ant so what does this millimeter means it turns out that there's nobody telling somebody who writes and makes a ruler what to write on that ruler so this particular ruler manufacturer decided that this millimeter correspond to the distance between the two smallest marks on their ruler right there those two smallest marks is one millimeter which means the distance between here and here if you were to count them is 10 millimeters or one centimeter and so we call this a centimeter ruler even though it's measured in millimeters according to the manufacturer now 10 right this is a 1 all right so that one actually means 10 millimeters that 2 means 20 millimeters so we actually have to know a little bit about what we're measuring in order for our measuring device to make some sense to us great so we've decided that these big units here are going to be in centimeters and so we're gonna measure everything in centimeters even though the ruler says millimeters now we could measure at millimeters we just have to multiply everything by 10 but I don't want to do that and so I'm gonna figure it out next numbers all right what are the numbers on here the numbers are from 1 to 2 2 to 3 so they're marked right sorry they're numbered every one centimeter and that turns out it's important for us to know that not so we can get the measurement right but so we can figure out what the marks mean because it turns out it's not these numbers that tell us how to accurately and precisely measure what we're measuring it's these little tiny marks that tell us that but in order to know what the marks are we have to know what the numbers are so here we go each number here is 1 centimeter moving along but now we're gonna look at these little marks I'm gonna zoom in this guy even more just like that and we've got the marks from 1 to 2 so this is one centimeter this is 2 centimeters what's in between what's that mark right there well first let's count we've got one tooth and this dot em 1 2 3 4 5 6 7 8 9 10 divisions so we've got a difference of 1 centimeter and it's divided by 10 divisions and if you do that you got zero point one centimeters per division so if I do this correctly I know that each one of those divisions is 0.1 centimeters so this first one here is not going to be 2 centimeters or 1.0 1 centimeters because each of these is 0.1 centimeter so this is going to be 1 point 1 centimeters how about this one here what do you think that one's gonna be hopefully you can't count it across and you came up with one point six centimeters okay so that's great we now know how to do that how would we do this one right there hopefully you're cutting them up with two point three centimeters so that's how we can figure out what each of those marks is and what each value is we can take the numbered divisions right those are the numbered divisions here we figured out the difference between them that one came from subtracting two minus one and then we divide it by how many divisions there are to figure out how what the distance is in between those divisions great so point one centimeters per division we can now identify any mark that we want to on this ruler so we're ready to measure the answers not quite yet okay so let's go over to our actual measurement and I'm gonna zoom this in again because it turns out the important parts in the details here so here we have the number six underneath my picture is the number seven if I take my picture it whoops if I take my picture away momentarily there's the number seven and so what is this one six point one centimeters remember when we have a measurement we always have a number and a unit we don't just have a number all by itself so six point one centimeters okay so you're like hey well when you told us a few slides ago right here's my at the end of my box all right this is six point five centimeters and this is six point six centimeters so isn't it somewhere around there isn't it somewhere around six point five or six point six and the answer is yes it's somewhere around there there it turns out we know a little bit more detail than just it's somewhere around there we know it's between six point five and six point six if you take this line from this box and extend it down it is definitely higher than six point five and it is definitely lower than six point six so we know it's somewhere between six point five and six point six and in fact since we know that it's between six point five and six point six we know it's going to be six point five something and what we can do is we can guess at that something now what do I always have to put two is units so I got to make sure to add those there so it's gonna be six point five something centimeters and we can actually make a vague guess at what that something is because this line right here that I drew in red is fairly far away from the six point five centimeter line and it's much closer to the six point six centimeter line so it's more than halfway halfway on a ten scale is five so we know it's more than a five is it a six or a seven there it's a guess and we call this our estimated digit in our measurement because it is a guess nobody knows what that is but you're gonna make your best estimate as to what it is and the person next to you well there might not be anybody next to you right now but if there was a person next to you measuring the same thing might might disagree with you on that last digit and that's okay because it's an estimated digit we know the six absolutely for sure we know it's a six we know the five the six point five we know that absolutely because that line definitely comes between 0.5 and point six but the next one is an estimated digit now I'm going to go ahead and call this a six point five seven centimeters but somebody might call it a six point five six centimeters and that would be perfectly okay and maybe even a six point five eight centimeters somebody might be able to justify that measurement so here we have three possible measurements for one measurement you're like I can't possibly be there third is a value of that measurement and you're correct there is a value of that measurement but here's the thing no one knows what that is no one knows what the actual measure it is right we can always get a better rule or a better rule or a better ruler we can always get one more digit one more digit one more digit and we can do that forever so it turns out that there's no way of precisely knowing a measurement you can't measurements are almost never exact and so what we're doing is we're making our best guess and these are all very valid possible guesses for this measurement so what did we do we figured out the units of our ruler we figured out the numbering on our ruler we figured out the marks on our ruler and then we measured so there's four steps to making a measurement most people put a ruler down they measure but it actually turns out you have to figure out a bunch of different things in order to measure precisely so that you get the right number of significant figures this has three significant figures but more generally we actually usually talk about digits well let me rephrase it let's keep that or if three significant figures and we have two digits after the decimal so it turns out that no matter what you ever read from this ruler you're always going to get two digits after the decimal I'm gonna move over to a spot we haven't drawn on yet here we're between the five and the six let's say I had a box that went exactly here what would I measure that box to be well you could say well this is five point one this is five point two is is five point three and there we go is five point four centimeters it's right on that so I'm gonna write five point four well if you write five point four what you're saying is I don't know much about that next digit I don't know if it's a three or a seven but do you like yeah it's right on there so what we have to do is we have to say five point four zero centimeters and mathematically those two numbers are the same but scientifically one has two significant figures and what it has three significant figures here we're saying I know that zero is pretty close to zero then the five point four were saying I don't know what that next digit is the hundredths it doesn't matter to me but every time we read this ruler we're going to get two digits after the decimal and so even when it falls exactly on the line we're going to get two digits after the so let's do one more let's say we had a box and it appeared exactly right on the floor there would you call that four centimeters or 4.0 centimeters or 4.0 0 centimeters which would it be well we figured out that our marks are every 0.1 centimeter and the rule is actually you're always going to read one digit after your smallest mark so if we draw a number line here since we are marked to the zero point one we can read to the next digit over which is 0.01 and we should always get two digits after the decimal so it's hard because you kind of want to just write a shorthand you're like four isn't for the same as four point zero zero but no because those significant figures those significant zeros tell us we know that's a zero we know that's a zero when you write four you could have been rounding for point one you could be rounding for point four and you're saying I don't know I don't really care about those next digits but if you know them and you can measure them then we should report them precisely so it turns out this is not just rulers any sort of what we call analog measuring device is going to need this sort of treatment so a graduated cylinder has all these numbers on here and these little marks between it you're going to have to look at it figure out its units figure out the numbers figure out the marks then read it because you can't read it until you know what you're trying to read you can't look at that graduated cylinder and be like oh it's you know eight point seven five four milliliters how many digits after the decimal did you know to look for and the example I give is let's say you were in a crowded room and before anybody could tell you anything somebody said oh close your eyes and then with your eyes closed tell me how many people in this room were wearing red if you never looked ahead of time to know how many people were wearing red how would you have even known to look for that and you're like well that's a stupid question you should have told me look around find how many people were in red then close your eyes and tell me the answer and that I could have done it well the same thing for measurements if you don't know ahead of time that I need to record this measuring device to two digits after the decimal to one digit after the decimal to four digits after the decimal or to the ones place then how are you gonna know how to record this measuring device so you have to look for those things first so you know what you're looking for when you do the measurement so if you're reading blood-pressure right that's an analog device that it turns out there's a correct way to do that know in a blood pressure nobody cares about those extra digits right so you don't have to worry too much about it but it turns out there's a correct way even your speedometer on your car there's a correct way all right these are our marked every 10 and if you're marked every 10 it turns out if you're marked here you can read here that means you can read this to the ones so it's really easy to identify 41 km/h verses 43 versus 45 and so you can do that on this particular device and here's another graduated cylinder they used to weigh babies by putting in these hill hanging scales and now they have digital ones but they just put them in these little hanging scales and there's a way to read that properly to those marks are not the only thing you can read you can actually read in between the lines so when people say hey read in between the lines that's actually what you're supposed to do when you're measuring is read between the lines so let's do a few more examples let's say we had a graduated cylinder and I can't draw to save my life so we're just going to draw a couple lines in a circle there and on that graduated cylinder you had some markings and they were labeled 30 40 50 then you had some small marks and looks something like that and on a graduated cylinder when we fill it with water it always makes this thing called a meniscus and a meniscus always has this curvature like that for water where it goes down because it turns out the water really likes the glass and so it tries to climb the glass but when we read water in a meniscus we always read from the very bottom of the meniscus sometimes we need to put our hand behind there to really see it and you'll see that and pictures that you get for this lab but how do we actually read this now my lines are not very well spaced but let's assume that they are so what do we do well the first thing we have to do is figure out the units I didn't write them up there but let's call this milliliters and it's always gonna be printed on your measuring device somewhere in your measuring device should be the unit's printed first then we do our numbers so we've got 10 milliliters in between our big divisions we figure out how many that's broken into 1 2 3 4 5 6 7 8 9 10 so 10 milliliters divided by 10 divisions is 1 milliliter per division so we know that each one of those marks is 1 milliliter so when we're trying to figure out where the bottom of this meniscus is we count from 32 31 2 3 4 35 36 37 38 so we know it's between 38 and 39 if it's between 38 and 39 it's going to be 38 something now how do we know how far to read it to do we just read it to 38 well we know because we always go off the smallest mark and the smallest mark here was one milliliter each one of those little tiny lines here is one milliliter that's our smallest mark and we can go one digit past that so if we do our little number line there's our mark there's what we can read it to so we can read it to one digit after the decimal or point one so what are we gonna do we're gonna zoom in on that even more it doesn't really let me too much and figure out about how far between 38 and 39 is that I see it's pretty close to 38 it's definitely less than halfway and in fact closer to the bottom than it is to halfway so maybe thirty eight point two milliliters one digit after the decimal all right here's one for you to try I'm gonna draw another meniscus all right there okay let's say I had that green meniscus and that green meniscus what would be my measurement so go ahead and pause it if you need to all right hopefully you counted through and you're said well that's a 35 and you didn't stop there because it looks like right it's right on 35 second just right 35 milliliters but remember we figured out that in this measuring device no matter what we're measuring since the smallest mark is one milliliter we can measure it 2.1 milliliters and if it's right on the line we're gonna call this 35.0 milliliters that green meniscus would be on 35.0 milliliters all right let's do another one let's say we had a measuring device we'll draw a box here for a measuring device and it was labeled like this so zero zero point one 0.2 0.3 0.4 and let's call this a decimeter ruler so they were labeled by 0.1 okay and that's all there was let's say that's what our measuring device was and we were going to try to measure a box here that went like that how would we go ahead and do that measurement well first thing figure out units that's decimeters down here so our units are decimeters then we figure out our distance between our numbers which is 0.2 minus 0.1 is 0.1 decimeters we figure out how many divisions that's broken into well there's no little marks here right there's nothing there's just these numbered lines so here our numbers are our smallest marks so this is just one division and so we know that each division there is 0.1 decimeters all right so if we are marked to 0.1 decimeters what can we read to the next digit after write marked 2 here read to here so we should be able to read this to 0.01 decimeters hey now when you first do this it seems like a lot of work to do all this figuring out marks and things like that after you've done it a hundred times you start to do this stuff in your head and I can look at a measuring device and just know fairly quickly what to read it to and I can do that in my head but for you I encourage you to write this stuff down look at the marks write down here's my smallest mark here's my number of divisions here's my value for each of these divisions here's what I should be able to read this to and you'll get some of the practice of that when you do the lab so I can read this to 0.01 so what I got to do is figure out how far between point two and point three mi but this is about halfway so I'm certainly more than halfway in fact I'd even say more than half halfway so I'm gonna call this box in Orange I'm going to call it zero point two right because we know it's between point two and point three and then my next digit is probably going to be an eighth decimeter 0.28 decimeters so that's what we'd get for a device that had no marks in between it now what I'm gonna do is I'm just gonna add some marks to this device so I'm gonna do it between point three and point four I'm gonna add some marks to this device one two three four five six seven eight nine it turns out by adding nine marks you make ten divisions you can count them if you want to and now let's measure a box that started at the same place the orange one did but now we've got a green one and I'm gonna measure that one right there how would we measure that box you're like well it's the same ruler so I'm gonna get the same answer all right it's just two digits after the decimal and then I just measure it but I changed my ruler right over here each division was 0.1 decimeters but what about in here now my divisions are smaller my divisions and you can do this work if you want our 0.01 meters 0.3 to 0.4 0.1 I divide that by 10 I get point o 1 decimeter per division now if I marked to 0.01 what can I read it to I can read it to 0.001 so just by adding those marks I actually get myself a whole nother digit of precision so the same look and ruler depending on how its marked can get you different levels of precision so what am I gonna do zoom in as much as I can on this guy here this is between point three and point four so we know it's going to be zero point three something we know each of these divisions is 0.01 so that's point three one point 3 to point three three point three four 0.35 0.36 so it's definitely between point three six and point three seven which means that's got to be a six now I know something about that next digit I know that it's not right at the beginning I know that it's not right at the end and so I can make an estimate and when I look at that it's just below halfway so I might say 0.63 I might say 0.636 four decimeters like that and so I get 0.36 for decimeters so without the marks I got two digits after the decimal with the marks I got three digits after the decimal and again this would be even if it occurred right exactly on a line if I had a box that went exactly to this point four that would be zero point four zero zero decimeters if those lines were there so that's another example I want to make one more example I'd say probably 90% 95% of the measurements you make it's really easy to break things into tens okay just really really easy to break things into tenths our brains are good at that because we have ten fingers but occasionally you run across a measuring device we're breaking into tens is just kind of difficult so what I'm going to do is I'm going to make a measuring device starting at zero here and then I'm gonna do this one too let's say this is going to be a centimeter measuring device now what I'm going to do is I have to zoom in on purpose 1 2 3 4 5 1 2 3 4 1 2 3 4 5 1 2 3 4 now let's see how two measuring device like this and now we're trying to measure a box on there you're like wow mark see a small I can't really see them very well that's absolutely right those marks are really small they're really close together which makes them hard to see however we can still do the same things we did before our smallest mark is - I'm sorry is 2 2 minus 1 equals 1 centimeter so it's marked to one centimeter numbered to one centimeter there's 10 divisions in between and so we get that zero point one centimeters per division and if it's marked to zero point one we should be able to read to 0.01 I'm sorry 0.01 yes so we know we should be able to get 0.01 centimeters of precision on this but it's really hard to see I mean I have to I have to lean over and look awfully darn closely to see what that is and you know I'm gonna zoom in because I can but right our eyes can't always zoom in sometimes we just have these small markings okay so what am i noticing here right I'm definitely between 1 & 2 so 1 point something 1.1 1.2 1.3 1.4 so this is going to be 1.4 and we know we should get another digit after that because we are mark 2.1 but without zooming in it's really hard to tell what that next stage is gonna be I'm not gonna be able to be like oh it's 1.4 one and be able to distinguish that well from 1.4 to so sometimes when these marks are really close together when it's really hard to estimate exactly how far it is between the marks what we can do is we can say hey look I can tell you if it's right on the mark or I can tell you if it's not on the mark and then our last digit either becomes a zero if we think it's right on that mark or a five if we think it's between two marks and so this one I might say it's one point four five centimeters but I'd be suspicious of anyone who said one point four six centimeters or one point four three centimeters I'd be saying you know I think you're trying a little too hard here and you probably if someone gave this to you again tomorrow you'd probably get a different number the point of this reading and learning this thing is so we can very consistently measure the same thing over and over again and get the same values every time all right so if you find marks that are really close together and really close together is maybe one or two millimeters spacing or less right then you might be trying that last numbers a zero or five it's on the line off line but in most cases you can estimate usually to the ones value in whatever that last digit it is there are some other exceptions your lab manual talks about them a little bit here and there if things are marked by twos or fives and you just have to make your best guess as to how to break things apart but most measuring devices are marked by tens and so this will cover 90% of the measurements you might ever have to make so you're gonna go ahead you're gonna work on the lab you're gonna try some of those measurements and see how you do remember this is a process of learning you've probably never had to measure like this before in your life so it takes some practice figure out the unit's figure out the numbering figure out the marks know what you're gonna read I'm always going to read two digits after decimal whether it's on a line offline anything I'm always reading two digits after a decimal then you make your reading and you write down a number with the correct number of digits and the right units and no matter what every time you use that same ruler over again if you've said I get to Judson after the decimal in this measurement then you get to digits after the decimal in every single measurement if you say I get one digit after the decimal in this measurement then you get one digit after the decimal in every single measurement there's consistency within a measuring device thanks for listening good luck