Isn't that rather the physicists way? Works well enough, used in a way not quite as intended by mathematicians, ...Disclaimer: I am physicist myself.

 Mathematicians' way:`````` Let a = distance in km; b = distance in mi; and φ = the conversion factor from mi to km. Then, a = φb.``````
 Ha, I saw a downvote there!I'm fine with that - on the condition that you never, ever treat a differential operator like a fraction again ;)
 Physicists have their own battles, like electrical engineers using Ohm's Law as a definition of impedance.
 What's the battle there? How do physicists define impedance?
 Ohm's law is an empirical law that only holds in certain circumstances. A classic exercise is measuring the current and voltage across a lightbulb, plotting it, and measuring the slope of the line. The slope is the impedance. Then you turn up the voltage and watch the line turn into a curve, which is where the law breaks down and doesn't apply anymore. The engineers treat it like a definition and assume linearity over all voltage.
 Wouldn't you start off using spherical cows?

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