To find the ratio $\dfrac{1}{3} : \dfrac{3}{8}$, divide the first by the second:

$\dfrac{1/3}{3/8} = \dfrac{1}{3} \times \dfrac{8}{3} = \dfrac{8}{9}$

So the ratio is $\dfrac{8}{9}$, which means $8$ to $9$.

You can verify: multiply both original fractions by 24 (the LCM of 3 and 8): $\dfrac{1}{3} \times 24 = 8$ and $\dfrac{3}{8} \times 24 = 9$. Ratio is $8:9$.