Today in my Physics lecture I suddenly thought of something. We all know that gravitational force is proportional to the two masses and inversely proportional to the square of the distance between them. So, naturally, there exists a system of natural units which equates the proportionality by setting $G=1$. Here I'm referring to Planck Units. But I realized that even though numerically using this system of units $F=\frac{m_1m_2}{r^2}$, dimension-wise that is wrong because the units do not correspond to the unit of force as defined by Newton's Second Law. Similarly, the electrostatic force, when making $k=1$, has the wrong unit as well. Why do we have to throw in those proportionality constants to convert the units? Shouldn't the units work out to be the same?
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