I wrote my entire physics thesis around a computer model of how laser light is scattered by a glass tube with inner and outer diameters in the range of the wavelength of the laser. Doing that with integers would have been challenging. My calculations were, necessarily, all approximations, but experimental physics tends to be all about approximations anyway. Over the range of values I was computing, a floating point value was more than precise enough. (I was using FORTRAN, but the issue is the same.)
Maybe it would help to understand what floats/doubles are good for if one thinks less about "accuracy" and more about "precision." In my program, say, the amplitude of scattered light at 90 degrees might have been computed as .7145523. But .7145523
what? Well, let's assume the units are something appropriate to light (watts maybe). Now, if the next discrete values above and below .7145523 that my floating point representation can encode are .7145524 and .7145522, that is more than precise enough for the purposes of my experiment. None of those three values is (likely to have been) the
exact wattage of the light scattered at 90 degrees, but I know that the precision of my calculation is about one part in ten-million. As long as the overall range of values I need to deal with doesn't take me out of that level precision (that is, if I also had to deal with values like 7.145523 * 10^48, subtracting a value near that isn't going to result in a value I can compare to, say, .7145523, because no floating point representation I've ever encountered retains precision at the seventh decimal place when storing really big values like 10^48), one part in ten-million is more than good enough for physics.
Another use I've made of floats is in computer art. I've written an insane number of programs that use sums of sine waves to modulate radial line
patterns, resulting in all sorts of (to me) pretty pictures. Again, the precision is more than good enough for that, and doing it with integers would be hard.
This one wasn't done by me, but by the college professor who taught me how to do them, 40 years ago: