in 2.4 is going to talk about length so you should watch the video before about by a meter is a meter and take your notes there the SI unit of the of length is the meter which is represented by the small letter M right here when we talk about length in meters we need to start talking about uncertainties so when we measure length you're going to measure it with some sort of scale you're going to use a tape measurer you might use a ruler if it's really small you could use like a protractor or something small but you're going to be using a scale when we measure length and with a scale you have uncertainty so uncertainty defines the resolution of your scale and we're going to be using this when we use either a ruler for length when we measure temperature with a thermometer or a graduated cylinder and what uncertainty is it says that you only precisely know the number of digits of a measurement to the smallest division of your instrument so if you have a ruler with lots of marks on it you can tell what your length is pretty precisely however if you have a ruler that only has two marks on it you cannot tell with as much certainty what your length is so the uncertainty is a way to define that mathematically so what we do is with for uncertainty we take them with the smallest division of your scale and divide it by half okay so we take the smallest division of our scale that we are using and divide it by half to find the uncertainty and it'll have the same units as your measurement so here's an example of a ruler on the bottom you can see here we're measuring this green line right here you can see the length is in they're in centimeters all right so this is one centimeter two centimeters three centimeters now we know more precisely we know that our length right here is going to be somewhere between two and three centimeters and if we count there's going to be 10 marks so one two three four five six seven eight nine ten marks between two and three so we know to every 0.1 centimeters that's the smallest mark on our ruler therefore the uncertainty right here if we look at it is going to be our smallest Mark which is 0.1 centimeters divided by 2 so that is equal you can plug this into your calculator or do it in your head 0.05 centimeters would be our uncertainty for this scale so let's go ahead and practice this so let's practice some length measurements including our uncertainty so you can see the ruler at the top has lots of all right so let's practice some length measurements so the ruler at the top you can see it's similar to the one on the previous slide it has marks every centimeter from 0 to 10 and it has 10 marks in between so that means that the smallest marks so the smallest Mark is going to be equal to here it's a little messy 0.1 centimeters okay so once again you can take half of that so just divide it by two either in your head or with a calculator and we know our uncertainty is going to be 0.05 centimeters so we already know what that's going to be now let's go ahead and actually look at the measurement here so we start at zero right you want to make sure that the the one end of your of your object is at zero the other end is that in between four and five it's going to be each one of these is 0.1 so it's going to be 4.1234567 and I'm gonna guess I'm gonna guess that's 4.7 now since we have marks every 0.1 you can estimate one more digit so we use our eyes to estimate do we think it's right at the line or maybe somewhere in between I'm going to say that it's kind of in between so I'm going to say that it's at 4.75 okay with our uncertainty Point 0.05 centimeters so when saying that we don't really know this last digit we estimated it all right so let's look at another example on the bottom here we're measuring a Tootsie Roll now you can see that the scale here is different we still have zero one two three four five ten up to 10 centimeters but we don't know any marks in between right so I'm going to we can know yes we can see that it's right at about maybe a tiny bit over three so our measurement is going to be three and then once again we get to guess one more digit looking in between three and four here do we think it's right at the line or do we think it's slightly over I'm going to say that it's just slightly over that it's like 3.1 now when our uncertainty is going to be different so the smallest the smallest division here is one centimeter right so our uncertainty is going to be half of that so it's going to just be one divided by 2 or 0.5 centimeters so since we don't have as many marks on our bottom ruler here we don't know our measurement quite as precisely and our uncertainty is going to be larger is that saying that we're less certain about what our measurement is all right we're going to practice this a lot in class