[Music] in this video we are going to discuss the definitions of precision and accuracy I will show you examples of the difference between precision and accuracy we'll talk about taking measurements on a ruler and how you must add an estimated digit to the end of every measurement and then we'll also discuss significant figures or as I typically call them sigfigs what exactly are significant figures and how can you calculate the number of sigfigs in a measurement okay let's get started definition of Precision Precision refers to how close together a series of measurements are to each other so that means that if you have several measurements and they are all very similar to each other then that set of measurements is precise accuracy refers to how close a measured value is to an accepted value that means that when the measurement agrees with the correct answer or the accepted value then that particular measurement is accurate so here are some examples if a dart board represents a Target and the bullseye would be an accurate measurement that Dart as well as these next three did not hit the bullseye so these are not accurate and because they are so spread out they're not close together these measurements are not precise so not accurate and not precise now we consider that these darts while they are not accurate because they're not hitting the bullseye they are close to other these measurements agree with each other so they are precise because they are close to each other but again they are not accurate because they did not hit the bullseye and finally in this scenario the darts are close together and they are on target they are on the bullseye so they are both precise and accurate well now that you understand the difference between precision and accuracy let's see an example with some numbers a woman gets on the scale and she wants to decide if the scale is an accurate scale so she decides to weigh herself on different scales and her actual weight is 110 110 lb so on the first scale as you can see from these four measurements these numbers are not close together and they are not except for maybe 107 is sort of close they are not close to her true weight which is 110 lb so like the first dartboard these measurements are not precise and they are not accurate if another scale gives her the following results when she steps on that same scale four times while yes these numbers are close together 149 and 150 her true weight is 110 so this particular scale is precise because of the consistent reproducible results that she's getting but it's not accurate this scale is off by 40 lbs basically finally if this scale gives her consistent readings that are close together 109 110 it's both precise and accurate because the numbers are close together and they are correct okay now we're going to talk about measuring objects on a ruler as you can see and this is a centimeter ruler it's not labeled as centimeters but that's what it is this pencil is larger longer than six cenm so we're not able to say it's 7 cm it's definitely 6 something and that's where the estimated digit comes in so I for example might call this 6.1 cm and as you can see the one is the final digit and that is considered to be the estimated digit now suppose that we're measuring an object where it falls on the line we still are unable to call this six we have to say more than that 6 point something in this case because it's exactly on the line then you would record this as 6.0 and the zero is at the end of the number and it is the estimated digit because it is on the line you add a zero at the end here we have a ruler that doesn't seem to have very many lines on it at all but it illustrates a point that I'd like to make about how you add an estimated digit in this case to record the length of the pencil based on the lines of the ruler we know it's going to be somewhere between 0 and 10 and that's all we know maybe it's 6 cm maybe it's 7 cm could we say 6.5 cm and the answer is no every line on this particular ruler is worth 10 cm so you would estimate to the one's place you estimate 1 power of 10 smaller than what the lines are worth so in this case we could say six we could say seven but that's we could do now suppose we have a ruler in which every line that's printed on the ruler is worth 1 cm we can estimate to the 10th place so perhaps you might call this 6 7 or perhaps you might call this 6.8 could we say that this ruler gives us a measurement of 6.75 and again the answer is no because every line is worth 1 cm so we can only put the estimated digit 1 power of 10 smaller than what these lines are worth so 6.7 6.8 but we could not go out to the 100th place we just don't have that level of precision with this ruler and now finally let's go to an even more precise ruler and measure the same object so as you can tell this ruler has every line is worth 0.1 0.1 cmers I'm going to give you a closeup of expanding what that looks like so we are now at a point where we can measure somewhere between 6.7 and 6.8 so let's say we think it's roughly about halfway between 6.7 and 6.8 you might say that the measurement is 6.75 or perhaps 6.76 but the final digit whatever that number is is the estimated digit and because every line was worth 0.1 CM the estimated digit was one power of 10 smaller than that particular measurement so we go out to the H hundredth place okay now let's consider some examples where the length of the object in some cases is exactly on the line remember we mentioned that we're going to have to add a zero if the first measurement is just six and we cannot say anything more than that because we are going only going to the ones place but now with this measurement we are able to go to the 10th place and let's take a moment to think about what that means I'm saying that 6.0 is a more precise measurement than just six it's a different ruler and therefore it does require a different level of precision so can you guess from this third ruler if we're going now out to the 100th place with our final digit this particular pencil on this ruler would be measured as hopefully you said 6.0 CM okay so that is the most precise of the three measurements I'm not changing the value it's still considered six on a calculator but in a science class 6.00 is a different number than 6.0 or just 6 and that leads us to our next discussion which is we'll be talking about significant figures okay so we're going to talk about significant figures now or sigfigs in a measurement the number of sigfigs include all of the known digits plus one estimated digit so in this example the measurement is 6.7 the known digit is a six because we estim estimated that final digit as a seven that counts as well it's all significant so this number would have two significant figures or two sigfigs for short in this example you can see that we now have a more precise ruler take a look at where the final estimated digit should be are we going to estimate to the 10th place or are we going to estimate to the 100th place hopefully you can see that because every line that's printed on this ruler is worth 1110th of a centimeter then we will estimate to the 100th place so therefore because it's exactly on the line it would not just be 6.7 we get to add a zero so 6.70 CM pay special attention to the fact that I had just shown you 6.7 on the previous slide and now I am showing you 6.70 so in this chemistry class 6.70 is more precise how many significant figures is a measurement of 6.70 three so this measurement has three significant figures not two it has three because we do count that final estimated digit and now I have to teach you some rules for determining the number of sigfigs in any measurement SigFig rule number one all nonzero numbers are significant so what does that mean it means any number from one through nine is going to be significant all the time so here I have a measurement 72.3 G there are no zeros everything counts this measurement has three sigfigs okay our next SigFig rule SigFig rule number two captive zeros are significant so what is that mean what are captive zeros a captive zero is a zero that is trapped in between nonzero digits here's an example 800.4 CM the eight we know that counts the four we know that counts and those two zeros are captive they are in between so everything counts in this measurement this measurement 800.4 has four significant figures okay on to SigFig rule rule number three if a number has a decimal point then the trailing zeros the zeros at the end of the number are significant so here is a number 1.00 it's a measurement 1.00 seconds it has a decimal point the zeros at the end are significant so therefore a measurement of 1.00 seconds has three Sig fix okay moving on on to SigFig rule number four if a number has no decimal point then the trailing zeros which are at the end of the number do not count they are not significant so notice the measurement 1,500 lers there is not an exact point there's no decimal at the end of a number so we have 1,500 or 1,500 but these two zeros are now no longer significant a measure measurement of 1,500 L has two sigfigs okay and our final rule SigFig rule number five leading zeros which are the zeros that occur at the beginning of a number typically this would mean you have a number that is less than one so leading zeros at the beginning of a number are not significant so we have a number that would be 0 0075 this measurement has three leading zeros but according to SigFig Rule Number 5 these are not supposed to count so therefore a measurement of 0.0075 M has two sigfigs okay so now the last thing I would like to show you if you are confused about all of those rules that you just saw and remember you are welcome to replay this video as many times as you like and you can pause the video to take notes I'm going to give you a little rule a pneumonic device for remembering the number of sigfigs in a measurement and I call it the Atlantic and Pacific rule so clearly you can see there is a Atlantic on the right and a Pacific on the left so here's the first application of the Atlantic and Pacific rule a number is given to you and we'll assume that's a measurement even though there's no unit let's just pretend that there's a unit ,200 something that could be seconds meters gr it doesn't matter I'm focusing on the number if a decimal is absent so a for absent a for Atlantic you will start counting from the Atlantic side of the number that is from the right skip over any zeros that you encounter on that side so I'm going to just cross them out and begin with the first nonzero digit so the first number I come to that's not a zero happens to be a two then continue counting every single digit no matter what it is 0 through 9 every single digit is now considered significant all the way until you get to the end of the number this measurement of ,200 has three sigfigs and this is according to the Atlantic rule you use the Atlantic rule when a decimal is absent let's go ahead and practice examples of the Atlantic rule so you'll have to forgive me for not showing you units all we have are numbers we have to assume that these were all measurements 200 it could be grams or meters that doesn't matter I'm just kind of focusing on the number right now every single one of these six numbers is going to obey the Atlantic rule because in every single number a decimal is absent so a for absent a for Atlantic if we count from the right side of the number and I'm going to go ahead and just skip over any of the Zer that are on that particular side of the number whatever we have left from that point forward from the end of the number is going to be the number of sigfigs so 200 has one SigFig 3,500 has two sigfigs 700,000 has only one SigFig now the next example it's 20,000 And1 there must be a reason for 20,000 And1 because it would be counted to the one's place for whatever reason the first number we come to on the Atlantic Ocean Side is a one so therefore since a one is significant everything else counts you may remember that that's the SigFig rule number two captive zeros are significant then we come to a number which is really large 6,200 ,000 if we skip over all of the trailing zeros because the decimal is absent we get only two Sig fix and then finally 8,300 the decimal is absent Atlantic Oceans side once we get to the three everything counts so this number has a total of four sigfigs so if the Atlantic rule applies when a decimal is absent we apply the Pacific rule when a decimal is present now we start counting from the Pacific Ocean or the right side excuse me the left side of the number so we count from the Pacific Ocean Side or the left side of the number skip over any zeros as we did before and once you come to a nonzero digit then you count every single digit all the way until you get to the end of the number so this particular measurement of 0.00250 contains three Sig PS according to the Pacific Rule and now it's time to practice the Pacific rule so all six of these measurements contain a decimal point we'll start counting from the Pacific Ocean or the left side of the number 200 with a decimal point at the end implies that you have confidence out to the ones place that measurement has three sigfigs 200.0 again because you're counting from the Pacific Ocean Side the first number you come to is a two and from that point forward everything counts so four sigfigs for that measurement similarly three is the first number we come to on the Pacific Ocean Side so everything counts four sigfigs but now what do we do with this next measurement 0.007 we have to skip over the leading zeros and this measurement only has one Sig fig our next example is 0.0020 once we get to the two everything Counts from that point forward that measurement has two sigfigs and then finally the first number we come to on the Pacific Ocean Side is a one so therefore it doesn't matter everything Counts from that point forward that measurement 1.20 contains five significant figures okay so now it's time to summarize what you learned in this video first I talked about the definitions of precision and accuracy we said that Precision applies when a set of measurements are very close together very similar to each other we said that accuracy is when a measurement is correct or very close to an accepted value when you take a measurement on a ruler you always must add an estimated digit at the end of the number which represents 1 power of 10 smaller than what those lines are worth on the ruler and in some cases when a measurement happens to fall exactly on the line then you would add a zero in the appropriate place as far as the decimal is concerned finally we talked about significant figures or sigfigs and we said that there were several rules for figuring out how many sigfigs there are in a measurement and I taught you the Atlantic and the Pacific rule to help you keep track of when the zeros count and when they don't so you may watch this video over and over to help you understand it and you may see me if you have specific questions