Which fraction converts to a repeating decimal number? OA. 1/12
OB. 7/8
OC. 14/25
OD. 17/20
OE. 6/10

Step-by-step explanation:

your answer is A, 1/12

Explanation:

Using a calculator shows that

We see that nearly all of the decimal values are terminating decimals. This means the decimals don't go on forever, so the decimals stop at some point.

Only 0.083333... goes on forever, so that's why 1/12 converts to a repeating decimal number.

A way you can determine this without a calculator is to use long division. Or you could use the idea that if the denominator has prime factors other than 2 and 5, then the decimal will repeat forever.

Note how the denominators of the fractions for choices B through E all have prime factors of either 2s only, 5s only, or a mix of 2s and 5s. This fact is why we have terminating decimals here.

In contrast, 12 has prime factorization 2*2*3. That 3 as a prime factor is why the decimal repeats forever.