 We've talked about precision and accuracy, and you can now begin to recognize sources of random and systematic error in your experiments. But when you take a measurement, or when you look at someone else's, how do you show the level of accuracy in the measurements? There are several ways. Here we'll look at the concept of significant figures, which will feature prominently in your work. Significant figures tell you about measurement error. Imagine you have a 50 gram mass. The value printed on the mass is 50G, 50 grams. But are you sure that's exactly 50 grams? It could be 46 grams, and they've just rounded it up to 50. In fact, it could be anywhere between 45 and 54 grams. Any of these values would round to 50 grams. So that measurement value has some uncertainty associated with it. Let's say it were printed 51 grams. This tells us something more. Now it can't be 46 anymore, because you can't round 46 to 51. But it could be between 50.5 and 51.4. That's at least tightened up the accuracy of our measurement. We now have a smaller range of error. OK, what if it were labeled 51.0 grams? This reduces the range of error even more. Now we know it's between 50.95 and 51.04 grams. And it's because that extra zero is specified after the decimal point. That zero says we measured this thing accurately enough to be sure that however you measure its mass, it's going to round to 51.0 grams. It might be 51.0398561 grams. It might be 50.99999 grams. But whatever it is, it's going to round to 51.0. OK, so the difference between those three values for the mass, 50 grams, 51 grams, and 51.0 grams, was the number of digits for which we were sure of the value. This is the basis of significant figures. Note that if we had absolutely no measurement error, then we could write the mass to an infinite number of decimal places. Exactly 51 grams would be written like that.