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Class 10MathematicsReal NumbersDecimal expansion of rational numbersHardLevel 20
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To write (\frac{1}{2^r5^s}) as a fraction with denominator (10^8) and an integer numerator, which condition is necessary?

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Answer and explanation

Correct answer: (r\leq 8) and (s\leq 8)

Step 1: (10^8=2^8\cdot 5^8). Step 2: The denominator (2^r5^s) must divide (10^8), so (r\leq 8) and (s\leq 8). Step 3: When converting to denominator (10^k), remember the divisor condition.

Related tags

Powers-Of-10Terminating-DecimalExponentsAdvanced

Frequently asked questions

What is the correct answer to this question?

(r\leq 8) and (s\leq 8)

Why is this the correct answer?

Step 1: (10^8=2^8\cdot 5^8). Step 2: The denominator (2^r5^s) must divide (10^8), so (r\leq 8) and (s\leq 8). Step 3: When converting to denominator (10^k), remember the divisor condition.

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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