In the US, prior to 1975, the official system of weights and measures was the avoirdupois system. Other weights and measures, specifically metric units, were defined in nice round terms of avoirdupois units. For example, a meter was defined as precisely 39.37 inches. In 1975, the US government officially adopted the metric system. The scientific world was already universally metric, so it needed no change. There was a metrication campaign, and millimeters appeared on our grade school rulers. But the ostensible ulterior motive, which was to cajole US industry into adopting metric product sizing for compatiblity with world markets, was largely a failure. The failure was popularly blamed on cultural resistance by the backward American public, but I submit it was largely due to industrial resistance to the costs of retooling. True, 2-liter soda bottles, 16mm film, and 195/55R16 tires showed up on the American scene, but for the most part manufacturers added parenthetical metric equivalents to their avoirdupois packaging ("12 oz (340 grams)"), and life went on with teaspoons, 7/16" socket wrenches and 12-foot two-by-fours. Perhaps the most significant change at that time was that the US government rebased its weights and measures in terms of metric units. So whereas previously, a centimeter precisely 0.3937 inches, so that an inch was a smidgin over 2.54 centimeters, the inch was now precisely 2.54 centimeters, making the centimeter a smidgimeter larger than 0.3937 inches. This was one small step for most of the US units, whose values adjusted slightly as they were rebased, but one giant leap for the final arbiter of US weights and measures, from the National Bureau of Standards (now NIST) in the US to the International Bureau of Weights and Measures (BIPM) in France. But I promised fun with sequence embedded decimals, so... Prior to 1975, a centimeter would have been an exact 0.3937 inches. This means that an inch would have been 1/0.3937 = 2.54 000508 001016 002032 004064 ... centimeters. Observe the nice doubling pattern of the 6-digit blocks. After 1975, the inch was precisely 2.54 centimeters. Now the centimeter is 1/2.54 = 0.3937 007874 015748 031496 062992 ... inches. Almost amazingly, we find the same 6-digit block doubling pattern here. Prior to the conversion, a centimeter was 0.3937 inches, post-conversion it was 1/2.54 centimeters. Perhaps, instead of letting either the avoirdupois or metric system dictate the conversion factor, we should adopt a compromise system whose conversion factors which are the geometric mean of the conversion factors of the two competing systems. In this new system, a centimeter would be sqrt(0.3937 * (1/2.54)) = sqrt(0.155) = 0.39370 039370 059055 098425 ... inches, and again we see curious relationships between blocks of 6 digits. Similarly, in our new system, the inch would be 1/sqrt(0.155) = 2.5400 025400 038100 063500 111125 ... centimeters. All this mathematical magic actually stems from an interesting factorization of a number near 500000. Perhaps you can find it.