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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 21
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After reducing (\frac{45}{2^5\cdot 3^2\cdot 5^4}) to lowest form, after how many decimal places will its decimal expansion terminate?

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Answer and explanation

Correct answer: (5)

Step 1: (45=3^2\cdot 5). Step 2: After cancellation, the denominator becomes (2^5\cdot 5^3). The larger exponent is (5), so the decimal terminates after (5) places. Step 3: Always reduce the fraction before counting decimal places.

Related tags

Decimal-ExpansionTerminating-DecimalCancellationReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(5)

Why is this the correct answer?

Step 1: (45=3^2\cdot 5). Step 2: After cancellation, the denominator becomes (2^5\cdot 5^3). The larger exponent is (5), so the decimal terminates after (5) places. Step 3: Always reduce the fraction before counting decimal places.

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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