Correct Answer:
D. -1
Explanation:
To determine if a fraction results in a terminating decimal without using a calculator, you must first simplify the fraction to its lowest terms. Once simplified, examine the prime factors of the denominator. In a base-10 number system, a fraction will only terminate if its denominator's prime factors consist exclusively of 2s, 5s, or a combination of both. This is because 2 and 5 are the only prime divisors of 10. If the simplified denominator contains any other prime factors, such as 3, 7, or 11, the division will result in a remainder that never reaches zero, creating a recurring or non-terminating decimal. For example, the fraction 3/8 terminates as 0.375 because the prime factorization of 8 is 2 x 2 x 2. Conversely, a fraction like 1/3 results in 0.333... because its denominator contains the prime factor 3.
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