this video is going to be a quick review of significant figures the first thing that you need to be able to do is determine how many significant figures are in a number so for example let's say if we have the number 846 how many significant figures are there every non-zero number is a significant figure so there's three significant figures in this number another example 3546 has four significant figures now let's say if we have a zero in between two non-zero numbers is that zero significant all zeros between two non-zero numbers will be significant so 704 has three significant figures 5006 has four significant figures now what about zeros to the right of a non-zero number like 500 how many significant figures are there in this number it all depends on if there's a decimal point or not if we do not have a decimal point the zeros to the right which are called trailing zeros are not significant so this would be only one significant figure in this case the trail and zeros are significant so this would be three significant figures likewise if we had 500.0 this would be four significant figures now what about the zeros to the left of a number like this point zero seven five are these zeros the leading zeros are they significant leading zeros are never significant so there's only two significant figures the seven and the five so let's say if we had point zero zero eight three six only these three numbers will be significant so to review let's try this example .0050830 how many significant figures are in this number so looking at the leading zeros remember the leading zeros are not significant the zeros that are in between two nonzero numbers those are significant and the trailing zeros are only significant if there is a decimal point which we do have therefore these five digits are significant so we're gonna have five significant figures so what i'm gonna do at this point is give you a quiz and i want you to determine how many significant figures are in the following numbers so the first one is going to be 42.50 and the second one is 7080 and then thousand fifty with a decimal point and then point zero zero seven zero three next we have point zero eight zero six zero and then 5030.0 and finally 750.064080 go ahead and determine the number of significant figures in each of those numbers by the way for those of you who want harder examples or maybe just more examples i have another video on youtube that is about an hour and a half long but it really goes deep into this topic so for those of you who want to master the concept of sig figs you can check out uh that video i'm gonna post the link in the description section of this video so feel free to take a look at that when you get a chance also if you're going to subscribe to this channel make sure to click the notification bell if you want to receive any updates of any new videos that i'm going to post in the future so let's go ahead and begin so four thousand two hundred fifty how many significant figures does it have so the zero at the right do we count it well it's a trailing zero and there is no decimal point so we're not going to count it so therefore we can only count these three nonzero numbers so we have three significant figures in the first example now what about the second example how many significant figures are there well once again we don't have a decimal point so we cannot count that zero but what about the zeros in between nonzero numbers so those zeros we can count so therefore this answer i mean this problem also have a three significant figures now for the next one there is a decimal point so the trailing zero is counted and all of the zeros in between the 3 and 5 are also counted so this example is going to have 5 significant figures for the next one we do have a decimal point but there are no trail and zeros we do have some leading zeros but those will not be counted so only these three digits will be counted so there's three significant figures in that number for the next one we do have a trail in zero which will be counted the leading zeros will not be counted so there's only four significant figures now in the next number 5030 we have a decimal point so all of the trailing zeros will be counted and the zero between the three and five that's always counted so we have a total of five significant figures for the last example all of the zeros in between the non-zero numbers are counted and since we have a decimal point the zero to the right is also counted so everything is counted in this example so there's let's see one two three four five six seven eight nine so we have nine significant figures for that problem now the next thing that you need to be able to do is you need to be able to round a number when multiplying or dividing so for instance let's say if we're multiplying 4.6 by 3.52 how can we round our answer with the appropriate number of significant figures well the first thing we need to do is perform the calculation so 4.6 times 3.52 if you type that into your scientific device your calculator will give you 16.192 now how should we round this answer to the appropriate number of significant figures what would you say what we need to do first is we need to determine the least number of significant figures in the first two numbers that we've multiplied already so in the first number 4.6 there's two significant figures in the second number 3.52 there's three significant figures so when you're multiplying or dividing you need to round your final answer to the least number of significant figures in the original numbers that you used to multiply to get your final answer so basically we need to round this answer to two sig figs so writing it from left to right we have the first digit which is a one and then the second one is a six now already this is two significant figures so the last number that we need to look at is the six should we keep it at six or should we round it up to seven and so we need to look at the next number if it's five or more then we need to round the six to a seven if it's four or less then we're gonna round down we're gonna keep the six and because it's four or less it's one we're going to round down so our answer is 16 rounded to the appropriate number of sig figs now let's work on some other examples let's multiply 5.64 by three point or rather let's choose a higher number by twelve point four five eight and let's divide ninety six point seven five two by three point go ahead and try those two examples round your answer to the appropriate number of significant figures so first let's type this in the calculator so 5.64 times 12.458 so the calculator gives us 70.26312 now the first number has three significant figures and the second number has five significant figures so we have to round our answer to the least number of significant figures so that's three so how can we round seventy point two six three one two to three significant figures so we're gonna need the first number the second one and the third one should we keep it a two or should we round it up to a three looking at the next number to the right of the two it definitely falls in the category of five or more so that tells us that we need to round up we need to round the two to a three so the answer for this example is 70.3 and it has three significant figures this answer has a total of seven significant figures now let's try the next example so let's begin by dividing 96.752 by three point five four one and so you should get twenty seven point three two three three five four nine eight now the first number has five significant figures and the second number has four so like always when multiplying or dividing you need to round your final answer to the least number of significant figures in this case four so looking at the fourth digit or the fourth significant figure starting from the left should we keep it at a two or should we round it up to a three so looking at the next number it falls in the category of four or less so we're going to keep the two so our final answer is 27.32 now let's talk about addition and subtraction but mostly addition so let's say if we wish to add 2.36 plus 12.1 how can we round our answer to the appropriate number of significant figures so if we add these two numbers this will give us 14.46 but what should we do here for this type of problem it's better to write the problem like this now you need to round your final answer to the least number of digits to the right of the decimal point so what i like to do is draw a line because for 12.1 there is no number to the right of the one and so we're not going to have any number to the right of this line but now if we add the two numbers it's going to give us 14.46 so what we're going to do is we're going to keep this significant figure but we need to determine if it should stay a 4 or if we should round it up to a 5. looking at this number it's greater than 5 so we need to round this number up so our answer is going to be 14.5 and that's how you supposed to do it when adding or subtracting let's try another example 4.328 plus 13 plus 5.45 so go ahead and try that problem well first we need to add so we have an eight two plus five is seven three plus four is seven and then four plus three plus five is twelve carry over the one and one plus one is two so we get twenty two point eight now what should we do next how can we round it so what we need to do now is determine which number has the least number of digits to the right of the decimal point and so that's the second number so we're going to draw the line here because it has nothing on the right side of that line so therefore our final answer should only contain these two digits but we're going to use the 7 to determine what we need to do to the 2. should we keep it a 2 or round it up to a 3 well seven is more than five so we're going to round the two up to a three so our answer is going to be 23 and that's basically it for this video so once again if you want more problems on significant figures check the link in the description section of this video for the other video where it's it goes into more detail on this topic thanks again for watching