9.4. Let the mass of the diamond be x, its cost is kx ${}^{2}$, where k is the proportionality coefficient. Let a piece with mass p break off from the diamond, then the cost of the broken part is kp ${}^{2}$, and the cost of the remaining part is k(x-p) ${}^{2}$. According to the problem:

$\kappa(x-p)^{2}=(1-0.36) \kappa x^{2}$

$\left(1-\frac{p}{x}\right)^{2}=0.64$
$1-\frac{p}{x}=0.8$

$\frac{p}{x}=0.2$

A fifth of the diamond broke off.
Answer: one fifth broke off