If {x} represents fractional part of x, then $\left\{\frac{5^{200}}{8}\right\}=$

If {x} represents fractional part of x, then

$$\begin{gathered} \frac{5^{200}}{8}=\frac{(25{)}^{100}}{8}=\frac{(1+24{)}^{100}}{8} \\ \Rightarrow \frac{5^{200}}{8}=\frac{1+\left({ }^{100}{C}_1\left(24\right)+....{+}^{100}{C}_{100}{\left(24\right)}^{100}.\right)}{8} \\ \Rightarrow \frac{5^{200}}{8}=\frac{1}{8}+\frac{24\left(integer\right)}{8} \\ \Rightarrow \left\{\frac{5^{200}}{8}\right\}=\frac{1}{8} \end{gathered}$$