Final answer:
To determine if a fraction converts to a repeating decimal, divide the numerator by the denominator using long division and check if there is a repeating pattern after the decimal point.
Step-by-step explanation:
A fraction that converts to a repeating decimal number is one in which the division result has a repeating pattern of digits after the decimal point. To determine if a fraction converts to a repeating decimal, you can divide the numerator by the denominator using long division. If the division result has a repeating pattern of digits, then the fraction converts to a repeating decimal.
For example, the fraction 1/3 converts to a repeating decimal: dividing 1 by 3 gives 0.3333... Notice how the digit 3 repeats infinitely after the decimal point.
In the options given, it is not clear what the actual fractions are, so it is impossible to determine which one converts to a repeating decimal number. More information is needed.
Learn more about Converting fractions to repeating decimals