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JGWeissman comments on Inverse Speed - Less Wrong
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For some reason no one does the obvious cancellation to end up in m^2. This even has an intuitive meaning, it's the cross-section that a line of fuel would need so that as you travelled along it you'd be "picking it up" at the same rate you were burning it.
"Miles per gallon"/"kilometers per litre" and their inverses are more convenient when people will be integrating that information with "dollars per gallon" / "Euros per litre" to get the information they really care about: how much they will be spending on fuel. "Gallons" / "Litres", though they are volumes, are being used abstractly to talk about an amount of gas, in the same way we could have abstractly used mass to refer to the same thing.