Which value of 'a' gives a result that fits within the condition on the decimal expansion?

To determine which values of 'a' fit within the conditions of decimal expansion, it's crucial to understand what is being asked regarding decimal representations, particularly in the context of repeating versus non-repeating decimals and fractional representations.

In this case, values like 2 and 7 might both lead to a specific type of fractional representation that can be expressed as a terminating decimal. For instance, if 'a' were representing a denominator in a fraction, values like 2 (which is a prime factor of 10) and 7 might yield different outcomes based on their prime factorization.

When you express fractions in decimal form, if the denominator, once simplified, contains only the prime factors of 2 (2^n) and/or 5 (5^m), the decimal representation will terminate. If it contains any other prime factors, the decimal will be repeating. In this scenario, both 2 and 7 can be valid representations, but they would work under different conditions.

Given this reasoning, it is clear that both 2 and 7 qualify based on how they could contribute to generating valid decimal expansions that either terminate or follow the established conditions of the problem. Therefore, the selection encompassing both these values aligns with the stated criteria, making