Final answer:
A fraction converts to a repeating decimal number if its denominator is not a factor of 10.
Step-by-step explanation:
A fraction converts to a repeating decimal number if it has a denominator that is not a factor of 10.
For example, let's consider the fraction 1/3. When we divide 1 by 3, we get the decimal 0.333333... which repeats infinitely. Therefore, 1/3 converts to a repeating decimal.
In contrast, the fraction 1/2 converts to a terminating decimal (0.5), not a repeating decimal, since 2 is a factor of 10 and the division can be done without any remainders.
Learn more about Converting fractions to repeating decimals