Write the repeating decimal as a fraction..27777777…

To write the repeating decimal .27777777... as a fraction, we can follow these steps:

Step 1: Let x be the repeating decimal. x = .27777777...

Step 2: Multiply both sides of the equation by 10 to shift the decimal point one place to the right. 10x = 2.7777777...

Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part. 10x - x = 2.7777777... - .27777777... 9x = 2.5

Step 4: Divide both sides of the equation by 9 to solve for x. 9x/9 = 2.5/9 x = 2.5/9

Therefore, the repeating decimal .27777777... can be written as the fraction 2.5/9.