Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point).

Answer 1

A rational number can be expressed as a repeating decimal if and only if its decimal representation is non-terminating and repeating.

To determine if a rational number can be expressed as a repeating decimal, we need to look at its prime factorization.

Prime factorization of 78: 2 * 3 * 13
Prime factorization of 512: 2^9
Prime factorization of 1725: 3 * 5 * 115
Prime factorization of 3140: 2^2 * 5 * 157

From the prime factorization, we can see that 78, 512, and 1725 do not have only 2's and 5's in their prime factorizations, which means they cannot be expressed as repeating decimals. However, 3140 can be expressed as a repeating decimal since its prime factorization only contains 2's and 5's.

Therefore, the rational number that can be expressed as a repeating decimal is 3140.