Question

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

• A. $\frac{1}{4}$
• B. $\frac{1}{8}$
• C. $\frac{3}{8}$
• D. $\frac{5}{8}$

Answer 1

The correct option is B $\frac{1}{8}$

$\frac{5^{200}}{8}=\frac{(5^2{)}^{200}}{8}=\frac{(1+24{)}^{100}}{8}$
$=\frac{1{+}^{100}{C}_1.24{+}^{100}{C}_2(24{)}^2+....{+}^{100}{C}_{100}(24{)}^{100}}{8}$
$=\frac{1}{8}+integer\Rightarrow \left\{\frac{5^{200}}{8}\right\}=\frac{1}{8}$