What type of decimal expansion will (\frac{13}{2^2\cdot 5^2\cdot 13^2}) have?
Answer and explanation
Correct answer: Non-terminating recurring
Step 1: The numerator (13) cancels only one factor (13) from (13^2). Step 2: The reduced denominator is (2^2\cdot 5^2\cdot 13). Since (13) remains, the decimal is non-terminating recurring. Step 3: Understand the difference between complete and partial cancellation.
Frequently asked questions
What is the correct answer to this question?
Non-terminating recurring
Why is this the correct answer?
Step 1: The numerator (13) cancels only one factor (13) from (13^2). Step 2: The reduced denominator is (2^2\cdot 5^2\cdot 13). Since (13) remains, the decimal is non-terminating recurring. Step 3: Understand the difference between complete and partial 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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