The submerged portion of a piece of pure ice floating in water is approximately:

According to Archimedes' principle and the law of floatation, the fraction of the volume of a floating body that is submerged inside a liquid is given by the ratio of the density of the floating body to the density of the liquid:
$$\text{Fraction of volume immersed }(f)=\frac{{\rho }_{\text{body}}}{{\rho }_{\text{liquid}}}$$

The density of pure ice (${\rho }_{\text{ice}}$) is approximately $0.917{\text{g/cm}}^3$ and the density of pure water (${\rho }_{\text{water}}$) is $1.0{\text{g/cm}}^3$.

$$f=\frac{0.917}{1.0}\approx 0.917$$

Expressing this fraction as a standard ratio approximation gives:

$$0.917\approx \frac{9}{10}$$

Thus, about $\frac{9}{10}\text{th}$ of the ice volume stays completely submerged beneath the surface of the water.