The decimal expansion for the rational number $\frac{11}{2^{3} . 5^{2}}$

will terminate after:

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One decimal place

Two decimal place

Three decimal place

More than 3 decimal places

answer is C.

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Detailed Solution

Concept-
In order to make the denominator a correct whole number, we shall first apply the exponent there.
We are aware that the square of 5 is 25, and the cube of 2 is 8.
We obtain

\frac{11}{2^{3} . 5^{2}}

\frac{11}{825}

by applying the exponent to the terms of the denominator.
The denominator terms are now multiplied, giving us the result

\frac{11}{2^{3} . 5^{2}}

\frac{11}{200}

.
We obtain

\frac{11}{2^{3} . 5^{2}}

= 0.055 when we divide 11 by 200.
The rational number's decimal expansion is 0.055, and it is obvious that it will end after three decimal places.
Hence, option 3 is the best choice.

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