Write the repeating decimal as a fraction..097097097…

To write the repeating decimal .097097097... as a fraction, we can follow these steps:

Step 1: Let x be the repeating decimal. x = .097097097...

Step 2: Multiply x by 1000 to move the decimal point three places to the right, since there are three repeating digits. 1000x = 97.097097097...

Step 3: Subtract x from 1000x to eliminate the repeating part. 1000x - x = 97.097097097... - .097097097... 999x = 97

Step 4: Solve for x by dividing both sides of the equation by 999. x = 97/999

Therefore, the repeating decimal .097097097... can be written as the fraction 97/999.