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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 19
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After how many decimal places will the decimal expansion of (\frac{81}{2^4\cdot 3^4\cdot 5^2}) terminate?

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Answer and explanation

Correct answer: (4)

Step 1: (81=3^4), so (3^4) cancels completely from the denominator. Step 2: The reduced denominator is (2^4\cdot 5^2). The larger exponent is (4), so the decimal terminates after (4) places. Step 3: First check cancellation of prime factors other than (2) and (5).

Related tags

Prime-CancellationDecimal-PlacesTerminating-DecimalReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(4)

Why is this the correct answer?

Step 1: (81=3^4), so (3^4) cancels completely from the denominator. Step 2: The reduced denominator is (2^4\cdot 5^2). The larger exponent is (4), so the decimal terminates after (4) places. Step 3: First check cancellation of prime factors other than (2) and (5).

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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