A rational terminating decimal is a decimal that ends after a certain number of digits. This occurs when a fraction is simplified and its denominator has only the prime factors 2 and/or 5.
Let's analyze the provided options:
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511: This is an integer and can be written as \( \frac{511}{1} \). It is a terminating decimal.
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5 over 11: This fraction does not have a denominator that consists solely of the prime factors 2 and 5. It results in a repeating decimal (approximately 0.4545...).
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√39: The square root of 39 is an irrational number, so it’s not a terminating decimal.
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√12: This can be simplified to \( 2\sqrt{3} \), and since it is also irrational, it's not a terminating decimal.
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1 over 3: This fraction results in a repeating decimal (approximately 0.333...), so it’s not a terminating decimal.
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7 over 8: The denominator (8) can be expressed as \( 2^3 \), which consists solely of the prime factor 2. Therefore, it is a terminating decimal (0.875).
From this analysis, the rational terminating decimals are 511 and 7 over 8.