 When talking about a physical quantity, we've already discussed the importance of choosing the right units and dimensions to describe that physical quantity, and also being aware of how accurate and precise your knowledge of that quantity is. And obviously making measurements is the right way to go about making sure you're right about all those details. But the next section is about the enormous and surprising power of guessing. It's amazing how well what we already know can be used to extrapolate to answer questions about things that we haven't thought about. But before we do that, we have to talk about scaling. Something scale just means its size. Often when we try and think about something unfamiliar, we can relate it to something that we are familiar with, but just it might be much bigger or smaller. For example, suppose I go to the shops, and I take a certain amount of money, and I buy a certain amount of chocolate. But I have dreams, and one day I dream of owning an entire truck full of chocolate. Now I've never experienced amounts of chocolate in that kind of quantity before at that scale. So I have to be a little bit careful about extrapolating my knowledge of how big a chocolate bar is and how much that costs all the way up to that scale. Now I've bought a lot of single chocolate bars, and so I know roughly how big a single chocolate bar is. A single chocolate bar here is something like 10 to 15 centimetres long. I don't know roughly how big a truck is. The business end of a truck is maybe 4 metres long. Sure, there are smaller and larger trucks, but that's how big a truck I want to fill with chocolate for my dream to be satisfied. So if I want to figure out how many chocolate bars fit into that truck, I say, alright, well it's 4 metres long. I'm trying to fit things that are 10 centimetres in there, so I should get this many along the bottom. And if I want to convert from centimetres to metres, which I'm going to need to do, that's going to be equal to... And remember, all I'm doing here is multiplying by one, so that's got to be right. I've got 100 centimetres in a metre, and so the centimetres cancel and the metres cancel and end up with a ratio 400 divided by 10, so I end up with 40. So I should be able to get 40 of those chocolate bars along the bottom of the truck. Does that mean I need 40 times as much money?