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To determine which fraction represents a terminating decimal, we need to examine the denominators of each fraction when they are in their simplest form. A fraction will represent a terminating decimal only if its denominator has no prime factors other than 2 or 5.

Let's analyze the given options:

1. **\( \frac{1}{3} \)**: The denominator is 3. Since 3 is a prime number and is not 2 or 5, \( \frac{1}{3} \) is a repeating decimal.

2. **\( \frac{3}{7} \)**: The denominator is 7. Since 7 is a prime number and is not 2 or 5, \( \frac{3}{7} \) is a repeating decimal.

3. **\( \frac{6}{19} \)**: The denominator is 19. Since 19 is a prime number and is not 2 or 5, \( \frac{6}{19} \) is a repeating decimal.

4. **\( \frac{9}{8} \)**: The denominator is 8. Since 8 is \( 2^3 \) (a power of 2), \( \frac{9}{8} \) is a terminating decimal.

Thus, the correct answer is **\( \frac{9}{8} \)**, which represents a terminating decimal.

Would you like any further details or clarification?

Here are some related questions you might find interesting:
1. How do you convert a fraction to a decimal?
2. Why do only denominators with factors of 2 or 5 give terminating decimals?
3. What is a repeating decimal, and how is it expressed?
4. Can fractions with large denominators still represent terminating decimals?
5. How do you determine if a decimal is repeating or terminating from a division?

**Tip**: For any fraction, if its denominator only contains 2's and 5's in its prime factorization, it will represent a terminating decimal.

Explore which fractions represent terminating decimals through an analysis of the prime factors of denominators. Learn why fractions like 9/8 have terminating decimals while others like 1/3, 3/7, and 6/19 do not. This guide is suitable for students in Grades 6-8, covering core concepts in number theory.

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