MP Board · Class 10 · Mathematics · Real NumbersThe decimal expansion of the rational number $\frac{33}{2^2 \times 5}$ will terminate after how many places of decimals?
The correct answer is B (2 places).
Explanation:\nTo make the powers of 2 and 5 equal in the denominator, we multiply the numerator and denominator by 5: $\frac{33 \times 5}{2^2 \times 5 \times 5} = \frac{165}{2^2 \times 5^2} = \frac{165}{100} = 1.65$.\nThus, it terminates after 2 decimal places (determined by the maximum power of 2 or 5, which is 2).
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.