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 \( 0.444\ldots \) given that \( 0.111\ldots = \frac{1}{9} \).

### Step-by-Step Solution:

1. **Understanding the Repeating Decimal**:
We know that \( 0.111\ldots \) means that the digit '1' is repeating indefinitely. It is given that \( 0.111\ldots = \frac{1}{9} \).

2. **Expressing \( 0.444\ldots \)**:
The decimal \( 0.444\ldots \) can be expressed as \( 4 \times 0.111\ldots \) because \( 0.444\ldots \) has the digit '4' repeating indefinitely.

3. **Substituting the Value of \( 0.111\ldots \)**:
Since we know that \( 0.111\ldots = \frac{1}{9} \), we can substitute this value into our expression for \( 0.444\ldots \):
\[ 0.444\ldots = 4 \times 0.111\ldots = 4 \times \frac{1}{9} \]

4. **Calculating the Final Value**:
Now, we multiply \( 4 \) by \( \frac{1}{9} \):
\[ 0.444\ldots = \frac{4}{9} \]

5. **Conclusion**:
Therefore, the value of \( 0.444\ldots \) is \( \frac{4}{9} \).