Question

If $\{ p \}$ denotes the fractional part of the number $p ,$ then $\left\{\frac{3^{200}}{8}\right\},$ is equal to

• A. $\frac{1}{8}$
• B. $\frac{5}{8}$
• C. $\frac{3}{8}$
• D. $\frac{7}{8}$

Answer 1

Answer: (A)

$\left\{\frac{3^{200}}{8}\right\}=\left\{\frac{\left(3^{2}\right)^{100}}{8}\right\}$
$=\left\{\frac{(1+8)^{100}}{8}\right\}$
$=\left\{\frac{1+{ }^{100} C _{1} \cdot 8+{ }^{100} C _{2} .8^{2}+\ldots+{ }^{100} C _{100} 8^{100}}{8}\right\}$
$=\left\{\frac{1+8 m }{8}\right\}$
$=\frac{1}{8}$