I'd avoid the rounding by using double digits...

3.14.15.9

3.141.59.27

But instead I would want a webserver on there that just serves up digits of Pi.

Twist: it serves up digits of e.

Twist: it serves up the first 10 digits of pi followed by e[10:].

Now that's just evil. (Better do it from the 100th digit or so to make it less obvious.)

It opens a stream á la websocket and just pipes digits down.

That would have a different answer based on whether you rounded or truncated. It would be 3.141.59.26 if you truncated.

It would also be 3.141.59.26 if you round half towards even.