Write the repeating decimal as a fraction..066866866…

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

Step 1: Let's assign a variable to the repeating decimal. In this case, let's call it x. So, x = 0.066866866...

Step 2: Multiply both sides of the equation by a power of 10 that will shift the decimal point to the right of the repeating part. Since there are three digits in the repeating part, we can multiply by 1000. This gives us 1000x = 66.866866...

Step 3: Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part. This gives us:

1000x - x = 66.866866... - 0.066866866... 999x = 66.8

Step 4: Solve for x by dividing both sides of the equation by 999:

x = 66.8 / 999

Step 5: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 66.8 and 999 is 1, so the fraction cannot be simplified further.

Therefore, the repeating decimal 0.066866866... can be written as the fraction 66.8/999.