How to expand $\pi$ in non-decimal bases?

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I was reading about $\pi$ converted into other base systems. We all know $\pi$ in base $10$:

$$\pi_{10} = 3.1415926535897932384626433(...)$$

but how has this been converted into, say, base $11$, where it reads:

$$\pi_{11} = 3.16150702865A48233(...)$$

I cannot get the process.

I know what base $11$ is but I thought the conversion were like $digit by digit". Yet just from the beginning something changes:

$3.14$ becomes $3.16$, but both $4$ in base eleven is still $4$.

How then has this conversion been made?