0.52525252 ......... is equal to

Options

A. `52/100`
B. `52/99`
C. `25/99`
D. `52/990`

Answer

To convert the repeating decimal \(0.52525252...\) into a fraction, we can follow these steps:

### Step 1: Let \(x\) be the repeating decimal
Let \(x = 0.52525252...\)

### Step 2: Multiply by a power of 10
Since the repeating part "52" has two digits, we multiply \(x\) by \(100\) (which is \(10^2\)):
\[ 100x = 52.52525252... \]

### Step 3: Set up the equation
Now we have two equations:
1. \(x = 0.52525252...\)
2. \(100x = 52.52525252...\)

### Step 4: Subtract the first equation from the second
Now, subtract the first equation from the second:
\[ 100x - x = 52.52525252... - 0.52525252... \]
\[ 99x = 52 \]

### Step 5: Solve for \(x\)
Now, divide both sides by \(99\):
\[ x = \frac{52}{99} \]

### Conclusion
Thus, the repeating decimal \(0.52525252...\) is equal to \(\frac{52}{99}\).