 If you get the number wrong you can still be close. If I say I'm about a meter wide, that's not great if I'm trying to make a well fitting suit, but it's fine if I'm trying to figure out how wide to make a doorway. But if I was to claim to be a vault wide, that is so deeply wrong that I couldn't possibly use that to do any kind of design. And the reason for that is that a vault is not a unit of length. So the idea of length is more fundamental than the idea of say a meter. And this more fundamental idea is called the physical dimension. So a measurement is describing some physical quantity and that physical quantity has a dimension and then we also describe it in a particular unit. So for example, one inch is equal to a certain number of centimeters. So the quantity on the left is a length and the quantity on the right is a length and length is the dimension. The inch part is the unit and the centimeter part is the unit and the dimension is length. And this equation is all right because it has a length equal to a length. You can't have a length equal to a time. That just doesn't make any sense. All right. And so this idea that all relationships between physical quantities had to have the correct physical dimensions, although it does seem kind of obvious, on the scale of human endeavor it's actually quite a new idea. It was only invented in 1822 by Joseph Fourier. And occasionally we still make mistakes along those lines. For example, in 2008 the Australian Capital Territory Government introduced the electricity feed-in bill. And the idea of this bill was to give people an incentive to put solar cells on the roofs of their houses by making sure that they got full price for the electricity that they generated. But in order to not distort the market commercially they put a cap on how many solar panels you could put on your roof and said that households would only get the full price if they had up to 10 kilowatt hours of generating capacity on their roof. The problem, a kilowatt hour is not a unit of power. It's a unit of energy. So power is defined as a certain amount of energy per unit time. And for a bunch of solar cells on a roof, a kilowatt is a very reasonable choice for a unit of power. And a typical solar installation on a roof might have something between two to eight kilowatts of capacity. In other words, under full sunshine you'd expect to date kilowatts of electricity to be generated. And so this legislation was probably meant to say that you get full price for electricity provided your total capacity was at or below 10 kilowatts. But it's not really the done thing to just kind of assume that when people write things in legislation they probably meant something else and so we'll go with that. And so this is a real problem. Kilowatt hours does come up in electricity bills quite a lot. If we just rearrange this equation we can see that if we multiply both sides by time then the energy you get is just the power times the time. And just as kilowatt is a reasonable unit for power coming off a roof and hour is a reasonable unit of time it turns out that the kilowatt hour is the unit of energy that electricity companies use to bill us. And so for example you might spend 20 cents per kilowatt hour for your electricity.