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Q.

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

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a

$\frac{1}{8}$

b

$\frac{5}{8}$

c

$\frac{3}{8}$

d

$\frac{7}{8}$

answer is D.

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Detailed Solution

Clearly, $3^{200} = 9^{100} = {(8 + 1)}^{100} = 8 λ + 1,$ where $λ$ is positive integer.
$∴ {\frac{3^{200}}{8}} = {\frac{8 λ + 1}{8}} = {λ + \frac{1}{8}} = \frac{1}{8}$

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If {p} denotes the fractional part of the number p, then {32008}, is equal to