I am going through concept of Random variable $X: \Omega \to \mathbb{R}$. So for fair dice we have
$$P(X=k)=\frac{1}{6}\;,\; \forall k \in \left\{1,2,3,4,5,6\right\}$$
hence $$E\left[X\right]=\sum_{k=1}^{6}k P(X=k)=3.5$$
Since $X$ takes integers but $E\left[X\right]$ takes non integer. Practically what is the importance of Expectation?