1.8 meters Since the ball loses 23.0% of it's energy with each bounce, that means that it retains 100% - 23.0% = 77.0% of it's energy per bounce. And since it bounces 3 times, that means that it will have 0.77^3 = 0.456533 = 45.6533% of it's original energy after the third bounce. So it will reach 45.6533% of it's original height after the third bounce. So 45.6533% * 4.0 = 0.456533 * 4.0 m = 1.8 m