The economy shrank at an annualized rate of 2.9% over one quarter. That's 2.9% / 4 ~= 0.7% in Q1.
If we assume the annualized rate, the economy would be 97.1% of its current size in a year. The fourth root is 99.267%, so the economy shrank about 0.733% this quarter. If it does so for four consecutive quarters, it will decrease by 2.9%.
I know that's what you said in the first place, but when extrapolating further into the future, it makes a difference.
If you calculate 1-(1-x)^(1/4), the difference between the true answer and x/4 is approximately 3 * x^2/32. For a figure of y percent, this is a relative error of 0.375 * y percent. Ignore it when y is small.
The GDP figure is only known to something like 1 or 2 decimal places.
sp332 uses the ~= symbols for approximately equal because technically you can't just divide the percentage by four like that. 2.9%/4 = .725% (exactly), but technically four quarters at .725% shrink each would produce 100%-((100%-.725%)^4) for the year, which is a 2.869...% decrease, not exactly 2.9%. But for small percents being compounded a small number of times it is a decent approximation, in this case thoroughly dominated by measurement inaccuracies and noise levels; the small percentage and the small number of compoundings work together to keep the error very small.
Anyways, for the reasons given above, it's indistinguishable. If the economy was changing rapidly enough for it to matter, well, since it can pretty much only shrink at sufficient rates to make a difference we'd probably all have better things to do than argue about compounding correctly...
But it is worth reminding people you can't do than in general, because it is easy to forget. See also the Rule of 72: http://en.wikipedia.org/wiki/Rule_of_72
It would be an extremely false statement to write, "The U.S. Economy contracted by 18.25% on Sunday before Thanksgiving", which is how our title reads. ("The economy shrank almost 3 percent in Q1").
The number 3% doesn't appear anywhere, just as the number 18.25% doesn't appear anywhere. sp332's very good point is that it should include the word "annualized" or read "0.7%". A huge difference!