Write the repeating decimal as a fraction..52121212…

To write the repeating decimal .52121212... as a fraction, we can follow these steps:

Step 1: Let x = .52121212...

Step 2: Multiply both sides of the equation by 100 to move the decimal point two places to the right: 100x = 52.121212...

Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part: 100x - x = 52.121212... - .52121212...

Simplifying the equation: 99x = 51.6

Step 4: Divide both sides of the equation by 99 to solve for x: x = 51.6 / 99

Step 5: Simplify the fraction: x = 86 / 165

Therefore, the repeating decimal .52121212... can be written as the fraction 86/165.