well hello and welcome to getchemistryhealth.com my name is dr kent and in this video i'm going to give you a quick introduction into how to make scientific measurements so of course in science we perform different types of experiments and when you perform experiments well you collect data and that data is then recorded somewhere so for example maybe you go in a lab you do an experiment and you write down 52.8 as your data or your measurement well what's wrong with this measurement well 52.8 watt right we need some kind of a unit so if you were to say 52.8 kilometers or 52.8 degrees fahrenheit or hours or minutes that would make a lot more sense so whenever you record a measurement in science you always have to record both the number and a unit now there are actually two different types of numbers that we work with in science the first type are known as exact numbers and exact numbers are those that have been defined to be true or those that you can obtain through counting so there's no kind of ambiguity there's no guessing there's no estimating there's no approximating for example one dozen has been defined to be exactly 12 it's not around 12 it is exactly 12 again it's been defined to be true one week is exactly seven days one dollar is exactly a hundred pennies one kilometer is exactly a thousand meters again these are all things that have been defined and i'm sure you can think of lots of others like for example one hour is exactly 60 minutes one minute is 60 seconds one foot is exactly 12 inches again these have all been defined so they're exact there's no estimating there's no approximating now exact numbers can also be numbers that you obtain through counting so you physically count one two three four five six seven so we know there are exactly seven quarters so we're not guessing we're actually defining how many quarters there are by contrast measurements are always inexact again when you're measuring something it's not been defined you're trying to determine what the value is and again the reason it's inexact is there's some kind of approximating there's some kind of estimating so for example maybe you measure the temperature of something and it's 82.4 degrees fahrenheit or you measure your weight on the bathroom scale and it comes up 178 pounds or you measure the length of a race and it's 100.0 meters these have all been measured so these are called in exact numbers we're not saying that person is exactly 178 pounds but they're approximately 178 pounds now when it comes to evaluating measurements we can evaluate them according to two different criteria the first one is known as the accuracy of the measurement and that's how close the measurement is to the target to the accepted value and the other one is the precision of that measurement and that's how close a series of measurements are to one another so for example if you're taking three or four or five measurements how close are all those measurements to one another so another way to think about this is accurate or accuracy is how correct your answer is how close to the true value is it and precision or being precise is how consistent you are so let me give you a couple examples just to help illustrate this so let's look at these four different targets a b c and d and we want to determine um which set of data or which set of these little blue shots or circles are accurate and precise which ones are accurate but they're not precise etcetera so again accurate means you are close to the bullseye you are right where you want to be that's the correct answer and precise means how close together how consistent is your data or your shots in this case so which of these are both accurate they're on target and they're precise they're very consistent they're very close together well of course it looks like d because you see they're on target and they're all close together so they're accurate and they're also precise they're also consistent so which of these is accurate but they're not consistent they're imprecise well that looks like b because you can see they are all then pretty close onto the target but they're more spread out they're not all clustered as close together as they were up on d now three which of these targets shows some data that is not accurate but it is precise so in other words it's very consistent but it's consistently wrong well that looks like c because you can see the data it's all clustered and very close together very consistent very precise but it's off target so it's not accurate and how about neither accurate nor precise or inaccurate and imprecise of course that must be a because they're all spread out and they're not on the target now let's try this with some actual data like you might see in the lab so here are four different sets of data a b c and d and it tells us that the true value is 55.4 kilograms so first we want to figure out which set of data is both accurate so it's close to our true value 55.4 and it's precise all the measurements are very close to one another so what do you think a b c or d well it looks like a because you can see the values are all very close to one another which means they're precise and when you average them out the average is very close or actually exactly on the true value so which of these are accurate but they're not as consistent they're imprecise well it looks like c because when you average these out yes you get a value an average here that's very close to the true value but the data is much more spread out you see here they're all they're all clustered close together 0.3.4.5 here it's ranges from 54.7 all the way up to 55.9 how about number three they're not accurate but they are precise or they are consistent well that looks like b because the average of these three values 54.9 is not on target right it's not real close to the actual value but they are very close to one another they're only off by 0.1 more here 0.2 more here etc so they're very close and then the last one d it's not accurate because the average of the three values is off target from the known value and they're all spread out too so that's inaccurate and imprecise so whenever you make measurements in science there's always going to be some degree of error associated with it you can't make a perfect measurement with no error so the more precise the measurement is well the less error is contained in it now error in a measurement is indicated by the number of what are called significant figures or significant digits so if a number has more significant digits that means it's more precise and has less error so let's talk about significant figures how do we record those so when you're making a measurement you want to record all of the known digits all the ones that are clearly marked on the device on the thermometer on the ruler on the graduated cylinder plus one final estimated digit so you only estimate one more digit beyond whatever is clearly marked this indicates the precision of a measurement now remember sig figs only apply to measurements right not to exact numbers again if something has been defined to be true like one foot equals 12 inches that is exactly 12 it is infinitely precise in other words there is no error in that whatsoever so let's just look at an example so here's a ruler and it's marked in centimeters we can see and we want to measure the length of this rod so what we do is we record whatever numbers are clearly marked on the ruler and then we're going to estimate one more digit beyond that so i can see it's clearly marked it's four point something and then i'm going to estimate one more so you might say 4.2 centimeters or maybe you think well i think it's closer to three so maybe you say 4.3 centimeters but what you don't do is you estimate more places than just one and say i think it's 4.217 you can only estimate one more digit beyond whatever is clearly marked on the device so this ruler is marked in ones so we can estimate out to tenths so 4.2 and that tells you then you're within plus or minus 0.1 so it might be 4.1 centimeter it might be 4.3 centimeter and those are all fine if you were to write down 4.3 i would write down 4.2 someone else would write down 4.1 those are all within the same realm of precision because they're all within 0.1 of the correct answer because again that last digit is the one you're estimating how would you make that measurement on this ruler so this ruler is more precise because it allows us to have more significant digits because this one is marked in one so four five six it's also marked in tens so here's 4.1 4.2 4.3 so now we can say okay i know it's 4 for sure and i know it's between 0.2 and 0.3 so 0.2 something for sure but again i always have to estimate one more so maybe i think it's right in the middle so i'm going to say 4.25 centimeters so up here we had 4.2 centimeters here we have 4.25 so you can see this one had two digits this one has three digits or three significant figures so more digits indicate that this value is more precise because this one we were estimating the hundredths place in this one on ruler a we were only estimating out to the tenths place so this ruler again gives us a more precise measurement and has less error in it because it produces values with more significant digits let's try that again on this paper clip how would you record the length of this paper clip on this ruler so again we see it's clearly marked in ones so i know it's between two and three so it's two point something but i have to estimate one more place again i can't estimate more or less than one so two point let's say three centimeters or maybe you say 2.4 centimeters again both of those answers are fine because we're both estimating in the tenths place now if you were to have a different place here and you were to say three point something that would be totally wrong because it's clearly two something now how about on this ruler well this one is marked in ones and tenths so again we can be more precise so now you might say well two for sure and then we see it's pretty clearly right on the three here so 2.3 but we can't stop there we have to go one more again if i were just to write this down as 2.3 that would say the ones are what i knew for sure but i'm estimating the tenths and that's not true because the tenths are marked so i have to estimate the hundredths so if you think it's right on the 3 you would say 2.30 or maybe you think it's slightly below so you might say 2.29 centimeters again those are both fine because we're both just off here in the hundredths place which is where that estimated digit is okay let's try a few more examples just to drive this point home how would you record the volume of the liquid in this beaker well again you want to record whatever place is clearly marked and estimate one more digit after that so here we see it's 20 something we're going to estimate one more looks like it's maybe 28 so 28 milliliters again if you say 27 or 29 that's fine because we all agree on the tens place it's the ones place that we're estimating now over here on this graduated cylinder you see now it's marked in ones so we know the ones for sure 28 something but again we have to estimate one more place so that would be tenths place so you might say 28.2 milliliters or maybe you think it's 28.3 milliliters again both are fine because we're estimating in the tenths place now now over here on the buret this is even more precise we're going to have more significant digits because now the ones are marked 28 29 30 and the tens are marked so 28.1 0.2 0.3 but again i still have to go one more so i know for sure it's 28.3 i'm going to estimate one more and say maybe two so 28.32 again if you think it's 28.31 that's fine because we're estimating out here in the same digit now notice how these values all got more precise so this one had two significant digits so it's the least precise then we went out to tenths place so that gave us three significant digits that's more precise and then four significant digits so that's more precise okay one last example let's go ahead and take a minute to practice reading the temperatures on these three thermometers so go ahead pause the video and just take a quick second and write down your three best guesses and then when you're ready to have your answers checked go ahead and hit play okay so what do we know for sure was marked in tens here's 20 here's 30 it's also marked in ones so 21 22 23 so i know for sure it's 21 point something but i have to go one more digit so maybe i think it's 21.2 and we'll assume this is degrees celsius since it doesn't tell us but if you said 21.3 again that's fine as long as we're estimating out in the tens 21 that would be completely wrong right because 21 would say tens are what i know for sure and i'm estimating the ones and that's not true i know the tens and the ones so i have to estimate tenths place how about over here on this thermometer well again tens are marked and ones are marked so i know it's 22 but again i can't just write 22 i have to estimate one more so if it's right on 22 then i have to put point zero one more time why would 22 be wrong because that would say you were estimating the ones place which is not the case we are estimating the tenths place because the ones are marked okay how about this last thermometer how would you do that well it's a little hard to see but we can tell tens are marked so i know it's 20 something ones are marked 21 22 and even the tenths so it's just above 0.1 but again i can't stop there i have to go a little farther so i'm going to say 22.12 degrees celsius you might say 22.11 degrees celsius or 22.13 degrees celsius but again we're all estimating out here in the hundredths place because we all agree that the tens the ones in the tenths are all clearly marked and the estimating has to occur in the hundredths place so which of these values is the most precise again the one that has more significant digits is more precise well i hope you enjoyed this quick video on how to take scientific measurements using the correct number of significant digits for even more videos on significant digits including how to use them in calculations please come visit me at getchemistryhelp.com