Rebalancing Ratio Conundrum

Schweser Problem: Want a Dollar Duration of $8.5 Million. Current MV=$105.133 Million. Current Duration is 8.25, which means current Dollar Duration=$8,673,500 (I guess Schweser rounded up). I would have used (MV New Portfolio)*(Old DD/New DD - 1) in order to find how much to sell, but they get a slightly different answer by using $8,500,000/$8,673,500=0.02 and multiplying that by the new MV of the portfolio. The answer is slightly different. should I still use the original (MV New Portfolio)*(Old DD/New DD)?