You're Elon Musk. You want to buy Twitter. You could offer $54 per share. Or $55 per share. But you offer $54.20 per share.

Hold that thought.

Most negotiations follow a common pattern. Say you list your house for $399,000. (After all, a price ending in 99 is supposed to make the house seem less expensive; since in the U.S. we read from left to right, we're more likely to use the first number -- in this case, the 3 -- to decide whether the price is reasonable.)

Since I understand the negotiation power of anchor setting, I offer you $350,000. 

Value consideration aside, making that offer is a bad move: According to a 2015 paper published by Harvard Business School, negotiators who make precise instead of round number bids achieve better outcomes

Experimental and field evidence from the real estate market suggest that the maker of the first offer may be able to further tilt the bargaining game to her advantage by expressing the offer price in precise terms.

For example, a list price of $1,020,000 is more informative and likely to lead to a smaller price adjustment than a list price of $1,000,000.

That's not just true for real estate. Take salary negotiations; research shows making a job offer using a precise dollar amount -- say, $81,600 per year instead of $80,000 -- causes the other person to feel you're highly knowledgeable about the job market and the value of the position. 

Which makes the other party assume there's less room to negotiate. 

The same is true for mergers and acquisitions, like Musk's purchase of Twitter. According to the researchers, investors who make "precise" bids for company shares yield better market outcomes than those who make round-number bids.

In short, using a precise number to indicate you are well-informed -- whether or not you actually are -- tends to tilt the negotiation your way. 

Instead of offering $350,000 for your house, I could have offered $352,300; that number implies I performed a thorough analysis. Maybe I evaluate a bunch of comps. Maybe I used an appraisal method like replacement cost or income capitalization.

Or maybe I'm just using a tried-and-true, research-tested negotiation strategy. Doesn't matter. 

Because it works. 

As long as you don't get too precise.

While the study found that most people aren't aware of the negotiating advantage of precise bids, an offer of $362,410.23 would seem not just goofy but suspicious.

If a bid is too precise, it may (seem) strategic to the recipient, rather than being driven by superior information. 

This may lead the recipient to rethink whether the bid is really informed.

So start using precise numbers when you negotiate, but not just to imply you've done your homework.

Use specific numbers because you've done your homework.

Because truly understanding the value -- to you and to the other party -- is the most powerful negotiating strategy of all.