After how many decimal places the decimal expansion of the rational number $\frac{23}{2^{2} \times 5}$ will terminate?

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answer is C.

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Detailed Solution

The given rational number is

\frac{23}{2^{2} \times 5}

.
Simplify the given number as follows,

\frac{23}{2^{2} \times 5} = \frac{23}{2^{2} \times 5} \times \frac{5}{5}

\Rightarrow \frac{23}{2^{2} \times 5} = \frac{23 \times 5}{4 \times 5 \times 5}

\Rightarrow \frac{23}{2^{2} \times 5} = \frac{115}{100}

\Rightarrow \frac{23}{2^{2} \times 5} = 1.15

Therefore, the decimal expansion of the rational number

\frac{23}{2^{2} \times 5}

will terminate after 2 places.
Hence, option 3 is correct.

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