There is no real reason to round off numbers up or down. I find that I am tempted to round off the recommendations of my newsletter when buying mutual funds. It tells me what percentage to invest. It seems strange to buy 1223.45 shares rather than, 1225 or 1223. In reality it cannot make much difference. So I usually just round it off to the nearest penny, which I suppose is what Watson would do.
When buying ETF's, which are usually not sold in fractional shares, I have found that a limit order a few cents below the bid price of the share is usually successful, because "full service brokers" seem to buy at whatever the market price happens to be.
When selling, I put in a price a few cents per share higher.
Most of the time, I manage to get my price.