zeros are they significant or not well the answer is that it depends there are a few rules that tell us when we can consider a zero to be significant and when we can't let's go through them right now here's the first one zeros sandwiched between nonzero digits are always significant what does this mean well it means let's say we have a number like 391 okay we know from what we've already learned that the three the n and the one are all significant and since the zero is sandwiched between them it too is significant so there are four significant figures in this number how about a number like 82,000 24 again 82 2 and four are all significant because they're nonzero numbers and since this zero is sandwiched between them it is also significant we have five total significant figures in this number now it doesn't just have to be one zero and it doesn't have to be in just one place okay so we can have a number like 109,000 and3 again 1 n and three are significant and since these zeros are sandwich between them they are all significant too so they're a total of six number of zeros doesn't matter number of groups of zeros doesn't matter and the other thing that doesn't matter is decimal points okay so we can have 5.63 or something like that and just as long as we have these significant figures and the zeros are in between them they're all going to be significant so this number here is going to have six significant figures so that's our first rule 0 sandwich between nonzero digits are always significant let's look at the next one this says here that zeros that come before all nonzero digits are never significant okay so an example of this would be 0.0000 4 91 all these zeros here come before the nonzero digits and obviously when I say before I mean to the left of so these guys are significant all these zeros come before them we don't even have to worry about them three significant figures total in this number another example could be 0.0132 two these guys are all significant but the zeros coming before them or to the left they don't matter they're not significant again only three as we've seen the significant figures problems before it doesn't matter how many you have right so it can be 0.0 00000000000000 62 and again these guys are significant but none of the zeros that come before them or to the left are significant we don't have to worry about anything any of them and this number only has two significant digits the six and the two okay so that was what happens when we have zeros that come before or to the left of a number zeros that come after or to the right of non-zero digits get a little bit trickier here are three examples all of them have a different number uh of significant figures or I should say we determine the significant figures in them different 83,000 83,000 which looks identical except I'm going to put a decimal place at the end of that and then let's say uh 83. so they all have 1 8 13 and three zeros but we apply different rules to each of them for the significant figures if we have zeros that come after nonzero numbers numbers and there is no decimal place in that number the Zer are not significant 8 and three which gives us two total here the other three zeros are not significant now we always ask our question is there a decimal point in this number okay here there wasn't so the zeros were insignificant ask it again 83,000 but with a decimal point at the end means that the zeros that come to the right of the nonzero digits are significant okay so that means that all five of these are going to be significant and our number has five significant figures the only difference is this decimal point right here it's here it's not here zeros that come to the right of nonzero figures are only significant if there's a decimal point 83. here are zeros coming to the right we ask our question is there a decimal point in the number yes there is so so in this case all three of these guys after the decimal point are significant again five significant figures in this number okay let's uh let's look at a couple more examples of this okay let's say we have um 4,000 500 uh 32,100 there's some zeros to the right of these nonzero digits so we ask ourselves is there a decimal place in the number no there's not and since there's not it means these zeros to the right of the non-zero digits are not significant 1 2 3 4 five is the correct number of significant figures here let's look at um 7890 0 0 again zeros to the right of nonzero digits is there a decimal place there is which means that these right hand zeros become significant six total significant figures here let's look at 90,000 90,000 significant figure 1 2 3 4 zeros to the right but there is no decimal point in this number so that means that none of these zeros are significant and there is only one significant figure here um 200 with a decimal place after it significant Zer to the right of it there is a decimal point so all three of them including the zeros are going to be significant lastly uh let's do 50.0 0 0 significant Zer to the right and since there is a decimal point all of these zeros are significant so we have five total significant figures here okay so it all boils down to if there are zeros coming to the right of non-significant of of nonzero digit it all boils down to is there a decimal point if there's a decimal point in the number the zeros to the right are significant if there is no decimal point in the number the zeros to the right are not significant I think the best way to learn this stuff is to go through a whole bunch of practice problems all right see a whole bunch of examples that's what we're going to do right now now you know if you've already got this down we go through a couple of examples just turn it off move on to the next video there's no need to uh to watch me do all these if you're having trouble though I think that we'll do enough problems that by the time this is over you'll have a really really good sense of when zeros are significant and when they're not