Number system and $\pi$

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Ok, we all use the decimal system with numbers from 0 to 9. And we have $\pi$ with an infinite number of decimals. We also have a boolean system or hexadecimal. Is there any decimal system where $\pi$ has an ending number of numbers?

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No -- since $\pi$ is irrational it does not have a terminating representation in any positional system whose base is an integer.

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The decimal system by definition has 10 digits, or at least this is my understanding. Do you mean perhaps a base (like binary, octal, hex, decimal) in which pi has a finite (an ending) number of numbers? If so, then e.g. base pi would do the job, though representing other numbers, like e, or ten (zehn, dix, ..) might be difficult in this system.