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Subjects
Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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For (\frac{41}{2^2\cdot 5^3}), what is the minimum value of (k) to convert the denominator into (10^k)?

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Answer and explanation

Correct answer: (3)

Step 1: The denominator is (2^2\cdot 5^3). Step 2: Since (10^k=2^k\cdot 5^k), the powers must become equal. The larger power is (3), so (k=3). Step 3: To form (10^k), make the powers of (2) and (5) equal.

Related tags

Powers-Of-10Terminating-DecimalReal-NumbersConceptual

Frequently asked questions

What is the correct answer to this question?

(3)

Why is this the correct answer?

Step 1: The denominator is (2^2\cdot 5^3). Step 2: Since (10^k=2^k\cdot 5^k), the powers must become equal. The larger power is (3), so (k=3). Step 3: To form (10^k), make the powers of (2) and (5) equal.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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