A $5\times 5$ matrix $A$ has singular values $\sigma_1 = 4$, $\sigma_2 = 2$, $\sigma_3 = 0.8$, $\sigma_4 = 0.1$, $\sigma_5 = 0.05$. When we construct the rank-3 approximation $A_3$ using only the three largest singular values and their corresponding singular vectors, the spectral norm $\|A - A_3\|_2$ equals: