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My response to "Why do Nikons use H 0.3, 0.7, 1.0 and 2.0 instead of ISO 12,500, 16,000 etc." were always answered with, "Because the ISO (International Standards Organization) does not recognize any film or digital speed higher that 10,000. So to avoid getting into trouble, Nikon uses the H designations."
Whoever told you that simply made something up that sounded logical instead of admitting that they didn't know the real reason. The reality is that any given sensor can only reach a certain range of ISO settings. Nikon refers to those ISO settings with numbers. However, sometimes you need either a lower or higher ISO than what the sensor can really reach, so Nikon offers the "L" and "H" ranges.
A D800, for example, has a native ISO range of 100 to 6400. The sensor cannot do any better than that. So, to shoot at "H1.0" (ISO 12800) the camera takes a shot at ISO 6400, but with a shutter speed that's twice as fast as it would have otherwise used. The resulting image is underexposed by one stop, and then the camera pushes the exposure by one stop to compensate.
That's why the camera refers to "H1.0" instead of ISO 12800: because you're pushing the best that the sensor can give you by one stop. And that also explains why both the "L" and "H" ranges offer reduced dynamic range compared to their nearest numbered ISO value. But you may still want to use them sometimes... knowing how they work, and what their pros/cons are, is part of knowing your tools as best you can to get maximum benefit from them.