smc

Adding $\sqrt{n-1}$ to both sides, we get $$\sqrt{n}<\sqrt{n-1}+\mathrm{0.01.}$$ Squaring both sides, we get $$n<n-1+0.02\sqrt{n-1}+0.0001,$$ which simplifies to $$0.9999<0.02\sqrt{n-1},$$ or $$\sqrt{n-1}>\mathrm{49.995.}$$ Squaring both sides again, we get $$n-1>2499.500025,$$ so $n>2500.500025$. The smallest positive integer $n$ that satisfies this inequality is $\boxed{2501}$.