Don't forget the decimals

$s=\dfrac{\theta}{360}(2\pi r)$ where $\theta$ is in degrees and $r$ is the radius of the circle

Convert $\dfrac{\pi}{5}$ to degrees. We have

$\dfrac{\pi}{5}\left(\dfrac{360}{2\pi}\right)=\dfrac{360}{10}=36$

Apply the formula,

$s=\dfrac{36}{360}(2\pi)(4) \approx \boxed{2.513}$