full text of the classic FAA guide
DENSITY AND HYPOXIA
Air is matter and has weight. Since it is gaseous, it is compressible. Pressure the atmosphere exerts on the surface is the result of the weight of the air above. Thus, air near the surface is much more dense than air at high altitudes. This decrease of density and pressure with height enters frequently into our discussions in later chapters.
The decrease in air density with increasing height has a physiological effect which we cannot ignore. The rate at which the lungs absorb oxygen depends on the partial pressure exerted by oxygen in the air. The atmosphere is about one-fifth oxygen, so the oxygen pressure is about one-fifth the total pressure at any given altitude. Normally, our lungs are accustomed to an oxygen pressure of about 3 pounds per square inch. But, since air pressure decreases as altitude increases, the oxygen pressure also decreases. A pilot continuously gaining altitude or making a prolonged flight at high altitude without supplemental oxygen will likely suffer from HYPOXIA—a deficiency of oxygen. The effects are a feeling of exhaustion; an impairment of vision and judgment; and finally, unconsciousness. Cases are known where a person lapsed into unconsciousness without realizing he was suffering the effects.
When flying at or above 10,000 feet, force yourself to remain alert. Any feeling of drowsiness or undue fatigue may be from hypoxia. If you do not have oxygen, descend to a lower altitude. If fatigue or drowsiness continues after descent, it is caused by something other than hypoxia.
A safe procedure is to use auxiliary oxygen during prolonged flights above 10,000 feet and for even short flights above 12,000 feet. Above about 40,000 feet, pressurization becomes essential.