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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 21
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If (n) is the smallest positive integer for which (\frac{n}{2^4\cdot 3^3\cdot 5^2\cdot 11}) has a terminating decimal expansion, what is (n)?

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Answer and explanation

Correct answer: (297)

Step 1: For a terminating decimal, the reduced denominator must contain only (2) and (5). Step 2: The factors (3^3) and (11) must be cancelled, so the least (n) is (3^3\cdot 11=297). Step 3: For the smallest value, cancel only the unwanted prime factors.

Related tags

Minimum-FactorTerminating-ConditionReal-NumbersHard

Frequently asked questions

What is the correct answer to this question?

(297)

Why is this the correct answer?

Step 1: For a terminating decimal, the reduced denominator must contain only (2) and (5). Step 2: The factors (3^3) and (11) must be cancelled, so the least (n) is (3^3\cdot 11=297). Step 3: For the smallest value, cancel only the unwanted prime factors.

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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