A rational terminating decimal is a number that can be expressed as a fraction \( \frac{a}{b} \) where \( b \) has only prime factors of 2 and/or 5 when fully simplified.
Let's analyze the options:
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13 - This is a whole number and can be expressed as \( \frac{13}{1} \), which is a terminating decimal.
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1 third (\( \frac{1}{3} \)) - This is a repeating decimal (0.333...), not terminating.
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78 - This is a whole number and can be expressed as \( \frac{78}{1} \), which is a terminating decimal.
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7 eighths (\( \frac{7}{8} \)) - This fraction has a denominator of 8 (\( 2^3 \)), which can be written as a terminating decimal (0.875).
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511 - This is a whole number and can be expressed as \( \frac{511}{1} \), which is a terminating decimal.
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5 over 11 (\( \frac{5}{11} \)) - This is a repeating decimal (approximately 0.4545...), not terminating.
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39−−√ (\( \sqrt{39} \)) - This is an irrational number, not a terminating decimal.
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12−−√ (\( \sqrt{12} \)) - This can be simplified to \( 2\sqrt{3} \), which is also an irrational number and not a terminating decimal.
Based on this analysis, the numbers that are rational terminating decimals are 13, 78, 7 eighths (0.875), and 511. The most direct and simplest examples are 13, 78, and 511 as whole numbers.
Choose any of these: 13, 78, or 511.