If p denotes the fractional part of the number p, then \ 3 ^ 200 8...

{ p }

denotes the fractional part of the number

p, then \left\{\dfrac{{3}^{200}}{8}\right\}

is equal to

Options

A $\dfrac{5}{8}$
B $\dfrac{7}{8}$
C $\dfrac{3}{8}$
D $\dfrac{1}{8}$

Correct answer

D. $\dfrac{1}{8}$

Step-by-step solution

${3}^{200} = {9}^{100}$

$⇒ ( 1 + 8{)}^{100} = 1 + C1 100 8 + C2 100 {\left(8\right)}^{2} + . . . {8}^{100}$
$⇒ {3}^{200} = 1 + 8\lambda$ , where $\lambda$ is some integer.
$⇒ \dfrac{{3}^{200}}{8} = \lambda + \dfrac{1}{8}$
$⇒ \left\{\dfrac{{3}^{200}}{8}\right\} = \dfrac{1}{8}$

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