0,9(4);

To convert the repeating decimal \(0.9\overline{4}\) (which means \(0.94444...\)) into a fraction, you can follow these steps:

1. Let \( x = 0.9\overline{4} \).

2. Multiply both sides by 10 (to move the decimal point one place to the right): \[ 10x = 9.4\overline{4} \]

3. Now, notice that \(9.4\overline{4}\) can also be expressed as \(9.4 + 0.0\overline{4}\). Let \(y = 0.0\overline{4}\):

   • So, \(10y = 0.\overline{4} = \frac{4}{9}\) (this is a known conversion).
   • Therefore, \(y = \frac{4}{90} = \frac{2}{45}\).

   Thus, we can write: \[ 10x = 9.4 + \frac{2}{45} = 9 + 0.4 + \frac{2}{45} = 9 + \frac{18}{45} + \frac{2}{45} = 9 + \frac{20}{45} = 9 + \frac{4}{9} \]

4. Substituting back: \[ 10x = 9 + \frac{4}{9} \]

5. To combine the terms on the right-hand side, express everything with a common denominator (9): \[ 10x = \frac{81}{9} + \frac{4}{9} = \frac{85}{9} \]

6. Thus, we have: \[ x = \frac{85}{90} \] Simplifying this gives us: \[ x = \frac{17}{18} \]

So, \(0.9\overline{4} = \frac{17}{18}\).