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If the decimal expansion of (\frac{13}{2^a5^b}) terminates exactly after (6) decimal places, which condition on (a) and (b) is correct?
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Answer and explanation
Correct answer: (\max(a,b)=6)
Step 1: The denominator has only powers of (2) and (5), so the decimal terminates. Step 2: The number of decimal places equals the larger of (a) and (b). For exactly (6) places, (\max(a,b)=6). Step 3: In such questions, use the larger exponent, not the sum.
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What is the correct answer to this question?
(\max(a,b)=6)
Why is this the correct answer?
Step 1: The denominator has only powers of (2) and (5), so the decimal terminates. Step 2: The number of decimal places equals the larger of (a) and (b). For exactly (6) places, (\max(a,b)=6). Step 3: In such questions, use the larger exponent, not the sum.
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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