Which denominator (q) can give a reduced fraction (\frac{p}{q}) whose decimal terminates exactly after (5) places?
Answer and explanation
Correct answer: (3125)
Step 1: For exactly (5) decimal places, the larger exponent of (2) and (5) in the reduced denominator must be (5). Step 2: (3125=5^5), so it gives (5) places. (250) and (40) give fewer places, while (1600=2^6\cdot 5^2) gives (6) places. Step 3: Compare the prime exponents of the denominator.
Frequently asked questions
What is the correct answer to this question?
(3125)
Why is this the correct answer?
Step 1: For exactly (5) decimal places, the larger exponent of (2) and (5) in the reduced denominator must be (5). Step 2: (3125=5^5), so it gives (5) places. (250) and (40) give fewer places, while (1600=2^6\cdot 5^2) gives (6) places. Step 3: Compare the prime exponents of the denominator.
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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