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For certain primes $p$, the average digit in the expansion of $1/p$ was foundto have a deviation from random behaviour related to the class number of theimaginary quadratic field $\mathbb{Q}(\sqrt{-p})$ (Girstmair 1994). In thisshort note, we observe that for the corresponding problem when we replace theintegers by polynomials over a finite field, there is never any bias. Theargument is elementary.

On the sum of digits of $1/M$ in $\mathbb{F}_q[x]$