$ \left\lfloor 10^{\lfloor n \rfloor} \pi \bmod 10 \right\rfloor $ - does this function give the nth decimal place of pi?

Question

Function to round the nth decimal place of pi to the nearest integer. For example, for pi, n = 0, y = 3. n = 1, y = 1. n = 2, y = 4. And so on and so forth.

Gives me good results until n = 17, which yields 8 instead of the expected 3. Then it's unfortunately kind of all over the place. It only gives me even numbers?

Is my function correct, or is this a Desmos error?

https://www.desmos.com/calculator/bekze2iayc

Answer 1

Your function is mathematically correct, but not computerically correct. $64$ bit floating point numbers have about $16$ decimal digits of precision. You don't need the floor on $n$, but you are trying to extract decimal digits that are not there.