Enrique says 0.ModifyingAbove 4 with bar is a rational number. Which of the following best describes whether Enrique is correct and why?

Question

Enrique is correct. Repeating decimals are rational numbers because they can be written as fractions. The number is actually equivalent to StartFraction 4 over 9 EndFraction.
Enrique is correct. Repeating decimals are rational numbers because they can be written as fractions. The number is actually equivalent to StartFraction 4 over 10 EndFraction.
Enrique is not correct. Repeating decimals are never rational numbers.
Enrique is not correct. Some repeating decimals are rational numbers, but this one is not.

Answer 1

Enrique is correct. Repeating decimals are rational numbers because they can be written as fractions. The number \(0.\overline{4}\) (which means that the digit 4 repeats indefinitely) is indeed a rational number. Specifically, it can be expressed as \(\frac{4}{9}\). Therefore, the first option is the best description:

Enrique is correct. Repeating decimals are rational numbers because they can be written as fractions. The number is actually equivalent to \(\frac{4}{9}\).