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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 20
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After how many decimal places will the decimal expansion of (\frac{18}{2^2\cdot 3^2\cdot 5^4}) terminate?

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Answer and explanation

Correct answer: (4)

Step 1: (18=2\cdot 3^2). Step 2: After cancellation, the denominator becomes (2\cdot 5^4). The larger exponent is (4), so the decimal terminates after (4) places. Step 3: Carefully cancel prime powers present in the numerator.

Related tags

CancellationDecimal-PlacesPrime-FactorisationReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(4)

Why is this the correct answer?

Step 1: (18=2\cdot 3^2). Step 2: After cancellation, the denominator becomes (2\cdot 5^4). The larger exponent is (4), so the decimal terminates after (4) places. Step 3: Carefully cancel prime powers present in the numerator.

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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