Research outlined at Influence at work suggests that pricing your service or product with a precise number (e.g. $1789) is likely to make your more successful than if you use a round number (e.g. $2000)
Those sellers given an initial offer that ended in a precise number were much more conciliatory with their counteroffers typically countering 10% – 15% away from the opening offer. However those offered $2000 on average countered with an offer representing a 23% difference
Buyers seem to think that more thought and preparation has gone into a proposal with a precise number.
Beyond your negotiations maybe using more precise numbers could help when it comes to managing projects and persuading people to complete tasks by a certain time and date. Rather than asking people to get back to you by the end of the week you might be more effective signaling a precise time e.g. “Please get back to me by 3.45pm on Thursday.
The blog post from which I took the quotes has been removed, but you can find the details (and more) in the the Small BIG by Cialdini and his colleagues.