Using long division,1⁄9 = 0.111…. Multiplying both sides by 9, we have1 = 9 × 0.111… = 0.999….Furthermore, becausex/x=1,9/9=1. However,1/9=0.111..., so multiplying the numerator by nine, and thereby multiplying the answer by nine, produces 0.999... in terms of decimals, but, in terms of fractions, a numerator that is equal to the denominator.