Platformer Game Physics

[2NywAqkS]

In a simple platform game I'm making, when the player lands after he jumps he goes a small amount into the floor (or platform). I understand this is because his downward velocity per frame is not perfectly rounded to the y coordinate of the floor.

Although I understand the problem I'm not sure how to fix it. I could work out the players next position and only move to it if it isn't under the floor's y position, but that would result in the player landing slightly above the floor.

Is there a way to make the player always land precisely on the floor?

Any help is much appreciated.
Thanks,
Rowan.

[Thumper]

Test for the players next position, and if it is below the floor, move him to the floor.

EDIT:

to back up my point (realizing it might be unclear)

void movementFunction()
{
    player.y = someCalculationToGetNewPosition;

    if(player.y < floor.y)
        player.y = floor.y

    drawScreen(); 
}

[Zhuge]

Yeah. Instead of moving them all the way into the floor or simply not moving them (so they are floating) move them until they hit the floor.