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Which number is a rational terminating decimal? sqrt 12, sqrt 39, 1/3, 5/11, 7/8
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GPT-4o mini
A rational terminating decimal is a decimal that ends after a finite number of digits. Only fractions in their simplest form where the denominator has only the prime factors 2 and/or 5 will result in terminating decimals.
Let's examine the given numbers:
1. **sqrt(12)**: This simplifies to \(2\sqrt{3}\) and is an irrational number.
2. **sqrt(39)**: This is also an irrational number since 39 is not a perfect square.
3. **1/3**: This is a rational number, but its decimal representation is \(0.333...\), which is a repeating decimal (not terminating).
4. **5/11**: This is a rational number, but its decimal representation is \(0.454545...\), which is also repeating (not terminating).
5. **7/8**: This is a rational number. The decimal representation is \(0.875\), which is a terminating decimal.
Therefore, the only number among those listed that is a rational terminating decimal is **7/8**.
Let's examine the given numbers:
1. **sqrt(12)**: This simplifies to \(2\sqrt{3}\) and is an irrational number.
2. **sqrt(39)**: This is also an irrational number since 39 is not a perfect square.
3. **1/3**: This is a rational number, but its decimal representation is \(0.333...\), which is a repeating decimal (not terminating).
4. **5/11**: This is a rational number, but its decimal representation is \(0.454545...\), which is also repeating (not terminating).
5. **7/8**: This is a rational number. The decimal representation is \(0.875\), which is a terminating decimal.
Therefore, the only number among those listed that is a rational terminating decimal is **7/8**.
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