Among (\frac{1}{18}), (\frac{1}{45}), (\frac{1}{72}), and (\frac{1}{90}), which has the most non-repeating digits before the recurring part?
Answer and explanation
Correct answer: (\frac{1}{72})
Step 1: The larger power of (2) or (5) in the denominator tells the delay before the recurring part starts. Step 2: (72=2^3\cdot 3^2), so it has a delay of (3) places. The others have larger exponent (1) or (2). Step 3: Understand the initial non-repeating part in non-terminating recurring decimals.
Frequently asked questions
What is the correct answer to this question?
(\frac{1}{72})
Why is this the correct answer?
Step 1: The larger power of (2) or (5) in the denominator tells the delay before the recurring part starts. Step 2: (72=2^3\cdot 3^2), so it has a delay of (3) places. The others have larger exponent (1) or (2). Step 3: Understand the initial non-repeating part in non-terminating recurring decimals.
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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