How long will it take before the orbit of the earth is 365 days exactly? I understand that the number of days per year has changed throughout the history of the Earth. Apparently there were once over 400 days per trip around the sun.
How long will it take approximately for the Earth rotation to slow some more to 365 days a year, with no extra time to make leap years?
 A: With the data you linked to: http://spacemath.gsfc.nasa.gov/earth/6Page58.pdf
A linear fit seems fairly reasonable for the given data, but using it to predict the near future is not really possible, since the data deviates from a linear trend a fair amount.
I used linear regression to get that the change in the number of days in a year versus the number of years from now (in millions) is given by $$\Delta D  = -0.13\Delta T$$
So if we let $\Delta D = -0.2425$, we get that $\Delta T = 1.87$. So we estimate it would take 1.87 million years to have exactly 365 days in a year, which is on the same order as the estimation made by babou (since we both assumed linearity).
However, as I said above, the data does deviate from the linear regression a fair amount. I found that the mean absolute difference between the linear regression and the data points was about 8 days (max = 19 days, min = 0.4 days), which is a lot more than the 0.2425 days that we are dealing with.
A: I've been out of school too many years to relearn Lagrange interpolation by hand but Wolfram Alpha will interpolate 5 data points before it breaks.  Using the 5 most recent data points in http://spacemath.gsfc.nasa.gov/earth/6Page58.pdf this gives an aproximation of

y=-3.2957×10^-9 x^4-5.02018×10^-6 x^3-0.00147727 x^2-0.147798 x+365.25

where y is the number of days and x is millions of years (today being x=0).  Solving this equation for y=365.0 gives x=1.66 million years.
