Constants in nature are irrational

If you look at all the constants that exist in nature, $\pi, e, \phi, \hbar$, etc, they are all irrational. Makes me wonder: is Nature not perfect? Is irrationality built into the Universe?

Or is the flaw in our number system? Could an alien civilization have a number system in which all of the natural constants are nice rational numbers?

According to me, that cannot be the case. We can approximate $\pi$ using a ratio. And a ratio will be the same in all conceivable number systems. So, maybe an irrational number will remain irrational. Am I wrong?

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