A rational terminating decimal is a fraction that can be expressed as a decimal that ends after a finite number of digits. This occurs when the denominator (in its simplest form) contains only the prime factors 2 and/or 5.
Let's analyze each option:
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7/8: The denominator is 8, which is \(2^3\). This fraction is a terminating decimal (0.875).
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12−−√: The square root of 12 is not a rational number. It is approximately 3.464, which is non-terminating and non-repeating.
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5/11: The denominator is 11, which has prime factor 11. This fraction is a non-terminating repeating decimal (approximately 0.4545...).
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39−−√: The square root of 39 is not a rational number. It is approximately 6.244, which is non-terminating and non-repeating.
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1/3: The denominator is 3, which has the prime factor 3. This fraction is a non-terminating repeating decimal (approximately 0.3333...).
From the options provided, the only rational terminating decimal is 7/8.