period of this signal it could be a donkey question but I'm a little confused.

I have this signal $w(t)=sin({\pi}0.1f)$. I have to calculate the period of this signal.

$w(t)=sin(2{\pi}\frac{1}{20}f)$

the period of this signal is: $20s$ while the frequency is $\frac{1}{20}Hz$

is it correct?
You are mostly correct.  The equation should be $w(t) = sin(2\pi\frac{1}{20}t)$.  The variable in the sin should be $t$, not $f$.  The frequency is determined by the $\frac{1}{20}$, not by the variable.

Other than that you are correct.  The period is 20s, which makes it a $\frac{1}{20}$ Hz sin wave.