The value of (0.333 ...... `xx` 0.444 .... ) is

Options

A. 0.148148 ...
B. 0.777 ...
C. 0.1212 ....
D. 1.333 ... .

Answer

To find the value of \(0.333...\) multiplied by \(0.444...\), we can follow these steps:

### Step 1: Convert the repeating decimals to fractions
The first number, \(0.333...\), can be expressed as a fraction. We know that:
\[ 0.333... = \frac{3}{9} = \frac{1}{3} \]

The second number, \(0.444...\), can also be expressed as a fraction:
\[ 0.444... = \frac{4}{9} \]

### Step 2: Multiply the fractions
Now, we need to multiply the two fractions we found:
\[ \frac{1}{3} \times \frac{4}{9} = \frac{1 \times 4}{3 \times 9} = \frac{4}{27} \]

### Step 3: Final Result
Thus, the value of \(0.333... \times 0.444...\) is:
\[ \frac{4}{27} \]

### Step 4: Convert the fraction to decimal (if needed)
To express \(\frac{4}{27}\) as a decimal, we can perform the division:
\[ 4 \div 27 \approx 0.148148... \]
This shows that \(\frac{4}{27} \approx 0.148148...\), which is a repeating decimal.

### Summary
The value of \(0.333... \times 0.444...\) is \(\frac{4}{27}\) or approximately \(0.148148...\).

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