The decimal representation of $\frac{11}{(2 ³ x 5)}$ will

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terminate after 3 decimal places

terminate after 2 decimal places

terminate after 4 decimal places

does not terminate

answer is A.

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Detailed Solution

Given expression is

\frac{11}{(2 ³ x 5)}

.
We know that, the decimal expansion of a given rational number is terminating, if the factors of the denominator of the given rational number are of form

2^{m} \times 5^{n}

, where n and m are non-negative integers.
Otherwise non terminating recurring.
As we can observe in the given expression, the denominator

2 ³ x 5

is of the form

2^{m} \times 5^{n}

.
So, the decimal expansion of the given expression terminates.
We also know, it terminates after k places of decimals where k is the larger of m and n.
In

2 ³ x 5

, m = 3 and n = 1.
Which implies, m > n.
So, the decimal expansion of the given expression terminates after 3 decimal places.
We can verify as follows,