If `(1)/(891)=0.00112233445566778899.......` Then what is the value of `(198)/(891)?`

Answer

To find the value of \( \frac{198}{891} \) given that \( \frac{1}{891} = 0.00112233445566778899... \), we can use the relationship between the two fractions.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
We know that:
\[ \frac{1}{891} = 0.00112233445566778899... \]

2. **Finding \( \frac{198}{891} \):**
We can express \( \frac{198}{891} \) in terms of \( \frac{1}{891} \):
\[ \frac{198}{891} = 198 \times \frac{1}{891} \]

3. **Calculating \( 198 \times \frac{1}{891} \):**
Since \( \frac{1}{891} = 0.00112233445566778899... \), we can multiply this decimal by 198:
\[ \frac{198}{891} = 198 \times 0.00112233445566778899... \]

4. **Performing the Multiplication:**
To make the multiplication easier, we can calculate:
\[ 198 \times 0.00112233445566778899... \approx 0.2222222222222222... \]
This is because \( 198 \) is approximately \( 200 \), and when multiplied by \( 0.00112233445566778899... \), it gives a repeating decimal.

5. **Final Result:**
Therefore, the value of \( \frac{198}{891} \) is:
\[ \frac{198}{891} = 0.222222222222... \]
This can also be expressed as:
\[ \frac{2}{9} \]

### Final Answer:
\[ \frac{198}{891} = 0.2222... \text{ or } \frac{2}{9} \]