Question

iliana was part of a group that was working on changing (0.overline{4}) to a fraction. each member of the group had a different answer. which answer is correct?
(\bigcirc \frac{2}{5})
(\bigcirc \frac{4}{10})
(\bigcirc \frac{4}{9})
(\bigcirc \frac{9}{4})

Explanation:

Step1: Recall repeating decimal to fraction

For a repeating decimal \(0.\overline{n}\) (where \(n\) is a single digit), the fraction is \(\frac{n}{9}\). Here, the repeating decimal is \(0.\overline{4}\), so \(n = 4\).

Step2: Apply the rule

Using the rule, \(0.\overline{4}=\frac{4}{9}\). Let's check other options: \(\frac{2}{5}=0.4\) (terminating), \(\frac{4}{10}=0.4\) (terminating), \(\frac{9}{4}=2.25\) (terminating). Only \(\frac{4}{9}=0.\overline{4}\).

Answer:

\(\boldsymbol{\frac{4}{9}}\) (the third option: \(\frac{4}{9}\))