Lay a long level "downhill" on the floor, with one end of the level on the level part of the floor and the other end at the lowest point. Raise the lower end of the level until the bubble is centered, then measure the distance from the bottom of the level to the floor to find the depth of the dip.
If the level isn't long enough, lay a flat board along the floor with a level on top. Raise the board until the level reads true, then measure from the dip in the floor to the bottom of the board.
Position the leveling strip on the floor and see if the top edge of the strip checks out as level. Adjust the strip as needed. When complete, this will be a spacer that bridges the gap between the old floor and the new, level surface.
To do this, simply cut several leveling strips the same size as the original strip. If the floor slants irregularly, cut strips that bridge the cap at each floor joist.
Attach leveling strips. Use screws to secure the leveling strips to the floor every 16 inches. Screw the strips into the floor joists or subfloor.