Given that `0.111……=1/9, 0.444` is equal to :

Options

A. `1/90`
B. `2/45`
C. `1/99`
D. `4/9`

Answer

To solve the problem, we need to find the value of \(0.444...\) (which is a repeating decimal) in terms of a fraction. We know from the problem statement that \(0.111...\) is equal to \(\frac{1}{9}\). We can use a similar approach to find the value of \(0.444...\).

### Step-by-step Solution:

1. **Let \(y\) equal the repeating decimal:**
\[ y = 0.444... \]

2. **Multiply both sides by 10:**
\[ 10y = 4.444... \]

3. **Subtract the first equation from the second:**
\[ 10y - y = 4.444... - 0.444... \]
This simplifies to:
\[ 9y = 4 \]

4. **Solve for \(y\):**
\[ y = \frac{4}{9} \]

Thus, \(0.444...\) is equal to \(\frac{4}{9}\).

### Final Answer:
\[ 0.444... = \frac{4}{9} \]