# Number system and $\pi$

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?

• No, only with number system with $\pi$ as a base. – m0nhawk Jun 4 '15 at 13:59
• No, because if we did then $\pi$ would be a rational number, which it is not. – Simon S Jun 4 '15 at 14:00

No -- since $\pi$ is irrational it does not have a terminating representation in any positional system whose base is an integer.
Note: Even some rational numbers have non-terminating expansions in base 10. For example, $1/3$.