What is the best estimate for 7.8 x 37.86?

To estimate 7.8 x 37.86, we can round each number to the nearest whole number:

* 7.8 rounds to 8

* 37.86 rounds to 38

Then we multiply the rounded numbers: 8 x 38 = 304

Therefore, the best estimate for 7.8 x 37.86 is $\boxed{304}$.