How many grains of sand on a beach? There's two reasons for answering this question. First, it will give us a useful way of imagining some large numbers. But there's a second reason. In physics and in other disciplines, we often have to make estimates in cases where we don't have the detailed data that could allow us to make a precise calculation. When the data are very approximate, we call it an order of magnitude approximation. We aim to get the exponent correct to get the answer to the nearest power of 10. The tilde, or squiggle, means on the order of or is very roughly equal to. The local beach for UNSW is Coogee. So how many grains of sand on Coogee Beach? If I know the volume of sand and the volume of a typical grain of sand, then I have the answer. Well, from walking along the beach, I know that it's about 400 meters long. Looking at it, I can see that it is - well, very roughly, 40 meters wide. I know that the sand must be more than a couple of meters thick, because big storms often shift the sand level a meter or two. But the sand can't be more than 10 meters deep, because I can see patches of rocks sticking up through it in places. So let's say it's very roughly three meters deep. I've ignored the volume of air between the grains, but this approximation is not as rough as some of the others I have made. So we take a sample of Coogee sand, put it on a ruler and take a photo using a microscope. These lines are at one millimeter separation. Again, very roughly, I estimate that a typical grain of sand has a volume like that of a cube with a side of 0.3 millimeters. So substituting the values, I give my answer as 10 to the 15. I've omitted the two from the calculation, because if I leave that two, you might think that I mean two rather than one or three. And as you know, my answer is just not even that precise. So I give the answer as on the order of 10 to the 15. Now a related question for you - which is greater, the number of grains of sand on the beach or the number of atoms in each grain of sand? Well, the best way to learn about estimation is to do it. So you'll answer that question in the next quiz. But before we go there, a few more words about this course. First, I hope that you've discovered from the little quizzes that doing is the most important part of learning. Don't be tempted to rush through the quizzes and also, look carefully at the answers afterwards, even if you were right. In the quiz about vectors, you probably needed pen and paper to draw sketches. In fact, if somehow you did quiz three without pen or pencil, I really doubt that you've learnt much about vectors and I'd advise that you go back and do it again. Drawing sketches is extremely important in physics; so much so that you can think of your pen and paper as your secret weapons. And one more thing. I recorded four little interviews with the aim of putting Newtonian mechanics, the subject of this course, into its prospective. We'll return later to talk about the limitations of Newton's laws, but two of these people can tell you a lot more. Professor Brian Schmidt shared the Nobel Prize for the discovery that the expansion of the universe is accelerating. Well, that discovery is certainly not what Newtonian gravity would predict. Professor Michelle Simmons is the director of our Centre for Quantum Computing and Communication Technology. She works in the quantum regime, where Newton's laws are largely irrelevant. But of course, Newtonian mechanics is superbly accurate over most of the problems that physicists and engineers work on. So I also interviewed Jasper Wolfe. He's an engineer at NASA who, among other things, uses Newton's laws to calculate the orbital decay of satellites. And Alex Bulgakov is a final year engineering student and also a racing car driver who uses Newton's laws, among other things, in race strategies. You don't need to view these, but you probably will find them interesting. How about saving them as a reward for after you've done the quiz and the test? Yes, there's another learning quiz with feedback and then the test for real marks. Take your time, relax and good luck.