解:$(3)$由题意,得$\sqrt {11}=100\sqrt {x},$两边同时平方可得$11 = 10000x$
即$x=\frac {11}{10000}=1.1×10^{-3}$
则$x$的值为$1.1×10^{-3}$
$ (4)$∵$\sqrt 6≈2.449,$$\sqrt {60}≈7.746,$$240 = 2^2×60,$$0.54 = 0.3^2×6$
∴$\sqrt {240}=\sqrt {2^2×60}=2×\sqrt {60}≈2×7.746 = 15.492,$
$\sqrt {0.54}=\sqrt {0.3^2×6}=0.3×\sqrt 6≈0.3×2.449 = 0.7347$