The precise number indicates confidence in my research and it gets past the other person's resistance point. They focus on the weird number rather the actual round amount. "And four hundred dollars? laughs I'm sure we can do that."
This is also a stronger negotiation tactic than asking for the whole amount. They offer 180k but you really want 210k? "To make me feel comfortable I'd need to see that number adjusted by thirty four thousand and six hundred dollars."
I am on the fence about numbers that are alliterative. They sound good, but they let people latch on to the sound which you don't want. You want them focused on the smaller number and get them to say "yes" to that, because then their brain won't let them say "no" after they've thought about it. In their mind, they are committed to that course of action then.
Also works for buying anything that you have to haggle over, like antiques, like the glass fronted antique cabinets we want. Four of them. $11,200 in total according to the ticket price. "Would you be willing to throw in all four for $8,760?" Slaps hand on desk as I say the final number. Sold! Lowest they could go was $10,500 just moments before.
Works every time, ninety percent of the time.