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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{16}{2^7\cdot 5^4}) terminate?

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Answer and explanation

Correct answer: (4)

Step 1: (16=2^4), so (2^4) cancels from the denominator. Step 2: The reduced denominator is (2^3\cdot 5^4). The larger exponent is (4), so the decimal terminates after (4) places. Step 3: Include powers hidden in the numerator during cancellation.

Related tags

CancellationPowers-Of-2Decimal-PlacesReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(4)

Why is this the correct answer?

Step 1: (16=2^4), so (2^4) cancels from the denominator. Step 2: The reduced denominator is (2^3\cdot 5^4). The larger exponent is (4), so the decimal terminates after (4) places. Step 3: Include powers hidden in the numerator during cancellation.

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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  7. 7Which of the following fractions will give a terminating decimal?
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