Why isn't it $E \approx 27.642 \times mc^2$?
Why is it that many of the most important physical equations don't have ugly numbers (i.e., "arbitrary" irrational factors) to line up both sides?
Why can so many equations be expressed so neatly with small natural numbers while recycling a relatively small set of physical and mathematical constants?
For example, why is mass–energy equivalence describable by the equation $E = mc^2$ and not something like $E \approx 27.642 \times mc^2$?
Why is time dilation describable by something as neat as $t' = \sqrt{\frac{t}{1 - \frac{v^2}{c^2}}}$ and not something ugly like $t' \approx 672.097 \times 10^{-4} \times \sqrt{\frac{t}{1 - \frac{v^2}{c^2}}}$.
... and so forth.
I'm not well educated on matters of physics and so I feel a bit sheepish asking this.
Likewise I'm not sure if this is a more philosophical question or one that permits a concrete answer ... or perhaps even the premise of the question itself is flawed ... so I would gratefully consider anything that sheds light on the nature of the question itself as an answer.
EDIT: I just wished to give a little more context as to where I was coming from with this question based on some of the responses:
<PERSON> comments:
You do have an ugly factor of $2.997458 \times 10^8 m/s$ in front of everything. You just hide the ugliness by calling this number c.
These are not the types of "ugly constants" I'm talking about in that this number is the speed of light. 453
It is not just some constant needed to balance two side of an equation.
<PERSON> answers:
It's all in how you define the units ...
Of course this is true, we could in theory hide all sorts of ugly constants by using different units on the right and the left. But as in the case of $E=mc^2$, I am talking about equations where the units on the left are consistent with the units on the right, irrespective of the units used. As I mentioned on a comment there:
$E=mc^2$ could be defined using units like $m$ in imperial stones ($\textsf{S}$), $c$ in cubits/fortnight ($\textsf{CF}^{−1}$) and $E$ in ... umm ... $\textsf{SC}^2\textsf{F}^{−2}$ ... so long as the units are in the same system, we still don't need a fudge factor.
When the units are consistent in this manner, there's no room for hiding fudge constants. 976