The greatest possible error is the largest number which is acceptable for estimation supposing the number is gotten by a rough calculation. It is typically calculated by half of the place value of the last digit of the number.
So in the measurement of 11 1/8 which is also equal to 11.125
The place value of the last digit is thousandth in place value or 0.001
Thus, the greatest possible error of 11 1/8 is 0.001/2 = 0.0005