For $1.3k5 < 1.33$, we need $1.3k5 < 1.330$.

Comparing digit by digit: $1.3k5$ vs $1.330$. The first two digits match ($1.3$). The third digit: $k$ vs $3$.

If $k < 3$: then $1.3k5 < 1.330$ regardless of subsequent digits. For example, $k=0$: $1.305 < 1.330$ ✓; $k=1$: $1.315 < 1.330$ ✓; $k=2$: $1.325 < 1.330$ ✓.

If $k = 3$: $1.335 > 1.330$. Not valid.

So $k$ can be $0, 1,$ or $2$ — all less than 3.

$k$ could be $0$ (less than 1) or $1$ (equal to 1) or $2$ (greater than 1). The relationship between $k$ and $1$ cannot be determined.