`3.bar(55)` in fractional form is -----

Options

A. `(357)/(99)`
B. `(352)/(99)`
C. `(357)/(90)`
D. `(354)/(90)`

Answer

To convert the repeating decimal \(3.55\overline{5}\) into a fractional form, we can follow these steps:

### Step 1: Define the repeating decimal
Let \( x = 3.55\overline{5} \).

### Step 2: Eliminate the repeating part
To eliminate the repeating part, we multiply \( x \) by 100 (since the repeating part starts after two decimal places):
\[ 100x = 355.55\overline{5} \]

### Step 3: Set up the equation
Now, we have two equations:
1. \( x = 3.55\overline{5} \) (Equation 1)
2. \( 100x = 355.55\overline{5} \) (Equation 2)

### Step 4: Subtract the first equation from the second
Now, we subtract Equation 1 from Equation 2:
\[ 100x - x = 355.55\overline{5} - 3.55\overline{5} \]
This simplifies to:
\[ 99x = 355.55\overline{5} - 3.55\overline{5} \]

### Step 5: Simplify the right side
Now, we can simplify the right side:
\[ 355.55\overline{5} - 3.55\overline{5} = 352 \]
So, we have:
\[ 99x = 352 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 99 to solve for \( x \):
\[ x = \frac{352}{99} \]

### Conclusion
Thus, the fractional form of \( 3.55\overline{5} \) is:
\[ \frac{352}{99} \]