Significant Figures

So here we're going to say that significant figures indicate the level of precision involved with measurements and recordings and when we get to ideas such as uncertainty, we'll see significant figures playing a bigger role. Now we're gonna say a number with more significant figures is more precise. Now we're gonna say determine the number of significant figures for any given value can be easy depending on how you do it. There's a lot of rules associated with significant figures. But to make it simpler for ourselves we'll break it down into two simple ideas and it has to do with the presence of a decimal point or not. So if we take a look here, we're gonna say for significant figures are first rule is this if your number has a decimal point you're gonna move from left to write removed from left to right. You're gonna start counting once you get to your first non zero number and keep counting until the end. So our first non zero number as we're moving from left to right, is this too? So that's where we start counting and we count all the way until the end. So 123. This would have three significant figures. Now if your number doesn't have a decimal point they're gonna move from right to left. We're gonna start counting again. Once we get to our first non zero number and keep counting into the end. So our first number here is five. So keep counting all the way into the end. So 1234, this would have four significant figures. And to keep significant figures easy for us to understand we're gonna go by these two simple rules. Now there'll be other things that pop up, which we'll talk about in the following example. But for right now, just realize that we have these two basic rules to help us with significant figures. Now that we've done that. Let's move on to our example.

So here we're gonna take a look at this example here it says, how many Sig Figs does each number contain? Alright, so for the first one we're starting out with 10.0 10 10 m because it possesses a decimal point we're gonna move from left to right. And we're gonna start counting once we get to our first non zero number. So here's our first non zero number. Once you start counting you count all the way until the end. So this would be 1234 Sig Figs for this particular value. For the next one We have 10,030 seconds it has no decimal point that we can see. So we're gonna move from right to left again. Start counting once you get your first non zero number which in this case would be the three and count all the way into the end. So 1234. So this would also have four sig figs. Next we have 2.00 times 10 to the three leaders. We don't worry about the base and our exponent, all we care about is the coefficient because this is written in scientific notation because it has a decimal, we're gonna go from left to right. Our first non zero number is this too? And we count all the way into the end. So 12366. Sing things. Now. Finally we have 14 people. Now this is what we call an exact number because you're not gonna have 14.1 or 14.30 people you're gonna have a whole number of people, an exact number of people. When we're dealing with exact numbers, there is actually an infinite number of significant figures. Now the chances of you seeing this, it all depends on your professor. But just remember when it comes to Sig Figs, we have two easy rules that we even remember in terms of decimal point or no decimal point. But when we're dealing with an exact number, there's an infinite ob series of sick fix. Because 14 people could be written as 14 people or 14.0 people or 14.0 people, all of them are saying the same thing. And because of that, there's an infinite number of sig fix. So just remember when we're dealing with uh an exact number, there's an infinite number of significant figures involved.

So when it comes to significant figures, if we're doing multiplication and division, it's the measurement with the least. Sig figs that determines the final answer. And if we're doing addition or subtraction then the measurement with the least number of decimal places. Yeah will determine the final answer. In this example here we need to figure out what our final answer will be with the correct number of significant figures. Where it's a combination of all of these different types of operations. So if we take a look here, realize that we have in parentheses 0.999 plus 1.1. Since they're adding it has to be the least number of decimal places here. This one has three decimal places and this one here only has two. So our answer at the end has to have two decimal places. When we add those together it gives me 2.009. But again we want only two decimal places so we'll have to round up So they'll give me 2.01 Times. This one here has one decimal place. This one here has three decimal places. So when we subtract them we need our answer at the end to have only one decimal place. When we subtract them. When we get initially is 14.285. We want only one decimal place. So rounds up to 14.3 divided by. All right. So now we're gonna have here uh this number here has two sig figs and this one here has two Sig figs. So when we multiply them we need a number with two sig figs. Plus this one has one Sig fig and this one has one Sig fig. So we have to add those two numbers together and by adding them together we'll get our new value which will come out initially as 30 .8 when we had those two numbers together actually 40.8, So then we have 40.8 here. Alright now we're adding these two together. This one here has one decimal place. This one here has two so we add those together, what we're going to get is 40.96 but again we only want one decimal place because they're adding together so we're gonna round up and it's gonna give me 41.0 on the bottom. Now if we check out each of these values, each of them has a decimal place. Right? So if we follow the rules that we learned up above, we have three sig figs for each of them. So that means our answer at the end has to have three significant figures as well. So when we punch that in we're gonna get 30.701049 but we want three sig figs so it's gonna come out 2.701 as my final answer. Mhm So just remember this is a quick refresher in terms of significant figures, analytical chemistry is all about precision and accuracy so we cannot forget some of these fundamental steps when doing any and all calculations that we will definitely be seeing as we proceed further and further into analytical camp. Mhm.

So here we continue with our discussion of significant figures here, it says read the water level with the correct number of significant figures. So if we take a look here, realize that when we're reading this, We see that the meniscus touches the line that looks like it's 20 ml. And realize here that we have these little hash marks. So this year would be 20 0.0 mls. That's because we have 10th place hash marks here. So the reading level, there is 20.0 mls, realize that there's a level of uncertainty with this last zero here, so to be as accurate as possible, we're gonna add an additional decimal place in order to make sure that it's more accurate. So here the best one would be option D 20.0 mls. So remember when it comes to reading the number of significant figures from any type of ruler or measurement, we always say that there is a level of uncertainty with that last digit. So we have to add an additional decimal place to get the right number of significant figures. Use this in practice to answer the next practice question below. So use what we just went over in order to answer this question, come back and see which answer I choose