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Uncertainty in Measurement

In chemistry, uncertainty is the expected error in a measurement, which is the difference between the value of a measured quantity and the value of the quantity as determined by the measurement process. Uncertainty is usually expressed in terms of standard deviation. Uncertainty can be quantified in several ways: for example, by using statistical methods, or by analyzing the variance of the individual measurements. The term "uncertainty" is also used in science and engineering in a broader sense, to indicate the lack of knowledge of either the value of a quantity or even its existence.

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Video Transcript

When you measure a physical value like mass or temperature, the value you obtained will have a certain degree of uncertainty. Uncertainty is limited by the tool you measure the physical value with which will have a certain amount of air. So, for example, I have these two different rulers, which can be used to measure different lengths. So let's say I want to measure some kind of length here on this ruler. So we know that this length is greater than one centimeter and less than two centimeters, and we know that it might be about maybe more than the halfway point. So we can guess that by using this ruler this length is about 1.6 centimeters. So we know that the one it's pretty certain because we know for sure that it is greater than one, however, were not entirely certain about the 10.6 value, since there are no tick marks to guide us where exactly this line sits between one and two. So this tells us that the one is certain, while the sixth is uncertain. However, when we go to the other ruler and let's say we want to measure some kind of length here, we know that the length is less than 0.5 centimeters, but we do know that this must be greater than 0.4 centimeters based on the tick marks on this ruler. And from here we would have to guess where this is on the ruler. And it looks like it's maybe about the halfway point, so we can say that this length is zero point 45 centimeters. So here we see that before is certain because we know that the length it must be greater than four. What was 0.4 centimeters? But the five is our guests, which is the uncertainty associated with this measurement. You'll see that depending on the type of tool that you use, you have uncertainty, um, at different points in your value. In this case, we have uncertainty in the 10th place, while in this ruler we have uncertainty associate at the 100th place. Significant figures are numbers that tell us information about uncertainty. The number of sick figs, for a certain value, show how certain a measurement is so iffy. Value has ah lot of sig figs. This means that the measurement is very accurate, while a number with less safe eggs means there is a higher degree of uncertainty associated with that value. So before going into the video, I want to briefly mentioned that whenever I use the hashtag symbol, I mean number. So for this video, I'll be talking about the different rules associated with Sig Figs that tell us how to treat numbers as significant numbers and which ones are insignificant. So for the first rule, it exact number has an infinite amount of, say, fix, um, due to counting or because it is a defined value. So, for example, let's say you have a dozen eggs in our language when we say Doesn't that means 12, So 12 has an infinite number of sick things associated with it. Let's say you have a pack of 100 con balls. 100 isn't really a defined value. But if we were to count a bag with 100 Conmebol's and obtained the value of 100 this still has an infinite amount of sick fix because we're able to count each hole cotton ball and for one more example, let's say you have one mile. This one mile is a defined value so this value has also an infinite amount of cigarettes. So Rule number two, a non exact number, has a defined number of Cygnus X. So let's say you take the mass of a pile of sugar and you obtain 3.586 g of sugar. This number has for sick fix, because each number contributes to one significant to figure. Here we have four digits, so we have for Sig Figs. As for another example, let's say you time something and you get 3.45 seconds. This has 366 because again, each digit contributes to one sigfig and here we have three digits. So we have 366 And for our last example let's say we measure the temperature of something and we get 547. Calvin. This value also has three digits and therefore has three Signet's. So that is rule number two. So So rule number three. Everything except zero is always so gonna begin, which is something that I alluded to in the previous rule. But essentially, whenever you see a non zero digit, you will count this as one cigarette. So if we will number four is your in between. Non zeros are always significant. So what I mean by that is that let's say let's take the year 2019. This number has forced a fix because there are four digits, and even though this digit is zero, it is in between two significant figures. So then the zero becomes significant, and therefore that means that the year 2019 has four significant figures. Now let's say you have, um, some kind of number like this. This would have six significant figures for the same reason the zero is sandwiched in between two significant figures. So then it becomes a significant figure as well. For the next rule, trailing zeros after a decimal point are significant. So this means that if you have some kind of number like so 0.500 this number has three sick fix because we have two trailing zeros after the five. As for another example, once a, you have 0.6 five five sierra. This number has four significant figures because there are three significant. It occurs here because thes air non zero values and it has one trailing zero. So then the total count is 466 So that is rule number five, you know through the sound once again. And so rule number six is that trailing zeros after a decimal point, but before a non zero number are significant. So let's say you have a number like zero point 0043 This number has two significant figures because first of all, there are two digits that are non zero numbers. That means right now are significant. Big account is to we do have trailing zeroes, trailing zeroes being defined as zeros. After the decimal point in this case, eso we do have trailing zeroes. However, it is before a non zero number. So these zeros are actually placement zeros, so they actually don't have any significance to them. So then they don't count and therefore it is only two. However, if you have a number like so, where you have trailing zeroes before the non zero numbers and after the non zero numbers, the significant figure count is four because you have your non zero digits. But you also have trailing zeros after the non zero digits, which brings up the council floor. But again, you have these placement zeros, which don't contribute to the significance of value. So then your total significant figure account is for and lastly, for Rule number seven, trailing zeroes for a number with noticeable point can be interpreted multiple ways. So, for example, let's say you have a number like So you can say that this has two significant figures because you have your two non zero digits here. But you can also say that it might have four significant figures. Um, if you imagine that there's a decimal point here because it's clearly not 43 is 4300. So then you can count the zeros, too. Eso depending on your professor. Uh, they may be picky about the number of sig figs that this has so be sure to ask, but in the next few videos I'll be treating the zeros as significant. Zero.