 We're going to start with a meter stick that's a rather roughly calibrated meter stick. There's only one scale division at the beginning and one scale division at the end. What we assume is that if we have a device, we can divide visually the smallest scale division into ten equal parts so that we can visually divide this into a tenth of a meter and estimate the nearest one of those. We're going to measure the distance between two lines with this meter stick. We'll estimate this distance to be about .3 meters. That is one significant figure and it's an estimated figure. The actual length might be .2 meters or it might be .4 meters, but our best estimate is to be .3 meters. We have one significant figure. If we report that piece of information as .30 meters, what we're telling someone is that we could actually visually divide this scale into a hundred equal parts and estimate that the nearest one of those. So basically say that it is the thirtieth one of those. That's really not practical given the calibrations on this meter stick. If we go to a second meter stick, this meter stick is calibrated to the nearest tenth of a meter. What that means is that we can measure with certainty the nearest tenth of a meter and then estimate between the smallest scale divisions and estimate to the nearest hundredth of a meter. If we measure our same distance, we find that we know with certainty that we are at least .2 meters and not up to .3 meters. So we're somewhere between .2 and .3 meters. We can estimate the second digit and say that we have .28 meters. The .2 we know with certainty. The .08 is estimated. We have a total of two significant figures, one certain and one estimated. Every time we increase the number of scale divisions on our device, we add another certain figure. We will always have one estimated figure as we estimate between the smallest scale divisions. If we take a meter stick with a hundred graduations on it, we're going to be able to know with certainty the nearest hundredth of a meter and then estimate to the nearest thousandth of a meter. We will have two certain figures and one estimated figure. So if we read our length now, we would know that we're between .28 meters and .29 meters. So we have two certain figures, .28 and one estimated figure, which I'll say is .8. So our distance is .288 meters. We have three significant figures, two certain, the .28 and one estimated, the .008. The number of significant figures you have is really determined by the calibrations on your instrument. Now I have another meter stick that I want to take that same distance with. If I put my meter stick up here this time, I come up with what looks like .34 meters. Well this is a little bit of a problem because my other meter sticks were telling me that was about .28 meters. Well if I look at my meter stick and I compare this meter stick with my previous meter stick, you can see where the problem is that one of my meter sticks is short and it's going to give me an error in my reading. One of the assumptions we make about instruments is that they're accurately calibrated. What we have is an inaccurately calibrated meter stick. Now this meter stick is not a terrible situation in the sense that if we find out that it's not accurately calibrated it introduces a constant error because it's always off by the same distance. So if we know that it's an error we might be able to correct our data later. A worst case scenario is a meter stick that looks like this and that it is warped in several different places. This will give us really inaccurate data and data that would be very hard to correct because the error in the calibration changes depending upon what part of the meter stick that you use. When you take measurements you want to make sure that you have an accurately calibrated instrument and that you notice the scale divisions and take the correct number of significant figures.