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After how many decimal places, the decimal expansion of the rational number $23 23 × 52$ will terminate?

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one decimal place

two decimal places

three decimal places

four decimal places

answer is C.

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Detailed Solution

Given the number is as follows,

23 23 × 52

.
We can observe that the denominator is

(23 × 52) = (2 x × 5 y)

, which means that the rational number terminates as it is multiple of 10.
Now to make the denominator a power of 10, we multiply the numerator and the denominator of the rational number by 5 and simplify as follows,
Question Image

So, the decimal expansion of the rational number is obtained as 0.115 which terminates after three decimal places.
Hence, the correct option is (3).

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