Write the repeating decimal as a fraction..522

To write the repeating decimal .522 as a fraction, we can follow these steps:

Step 1: Let x = .522

Step 2: Multiply both sides of the equation by 1000 (since there are three decimal places) to eliminate the decimal:

1000x = 522

Step 3: Subtract x from both sides of the equation to isolate the repeating decimal:

1000x - x = 522 - .522

999x = 521.478

Step 4: Divide both sides of the equation by 999 to solve for x:

x = 521.478 / 999

Step 5: Simplify the fraction if possible:

x = 521478 / 999000

Therefore, the repeating decimal .522 can be written as the fraction 521478/999000.