The decimal expansion of the rational number $\frac{33}{2^2 \times 5}$ will terminate after how many places of decimals?
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Question

The decimal expansion of the rational number $\frac{33}{2^2 	imes 5}$ will terminate after how many places of decimals?

Accepted Answer

The correct answer is B (2 places). Explanation:
To make the powers of 2 and 5 equal in the denominator, we multiply the numerator and denominator by 5: $\frac{33 	imes 5}{2^2 	imes 5 	imes 5} = \frac{165}{2^2 	imes 5^2} = \frac{165}{100} = 1.65$.
Thus, it terminates after 2 decimal places (determined by the maximum power of 2 or 5, which is 2).

Real Numbers

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