If (n) is the smallest positive integer for which the decimal expansion of (\frac{n}{2^3\cdot 3^2\cdot 5\cdot 7}) becomes terminating, what is the value of (n)?
Answer and explanation
Correct answer: (63)
Step 1: For a terminating decimal, the reduced denominator must contain only (2) and (5). Step 2: The denominator has extra prime factors (3^2) and (7), so (n) must contain (3^2\cdot 7=63). Step 3: When the smallest value is asked, cancel only the unwanted prime factors.
Frequently asked questions
What is the correct answer to this question?
(63)
Why is this the correct answer?
Step 1: For a terminating decimal, the reduced denominator must contain only (2) and (5). Step 2: The denominator has extra prime factors (3^2) and (7), so (n) must contain (3^2\cdot 7=63). Step 3: When the smallest value is asked, cancel only the unwanted prime factors.
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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