This table converts fractional 16ths of an inch into decimal inches and centimeters.
inches centimeters 1/16 0.0625 0.15875 1/8 0.125 0.3175 3/16 0.1875 0.47625 1/4 0.25 0.635 5/16 0.3125 0.79375 3/8 0.375 0.9525 7/16 0.4375 1.11125 1/2 0.5 1.27 9/16 0.5625 1.42875 5/8 0.625 1.5875 11/16 0.6875 1.74625 3/4 0.75 1.905 13/16 0.8125 2.06375 7/8 0.875 2.2225 15/16 0.9375 2.38125
Note that the equivalents in centimeters are exact, as one inch is 2.54 centimeters long. In the U.S., before 1964, it was instead the case that a meter was exactly 39.37 inches long, making the inch slightly larger than 2.54 centimeters; and in the British Commonwealth, the inch was slightly smaller than 2.54 centimeters, being defined on the basis of an independent physical standard.
As typewriters typically print with six lines to the inch, another group of fractions of an inch is often used. Here, even the decimal inches usually cannot be exact
inches centimeters 1/6 0.1666667 0.4233333 1/3 0.3333333 0.8466667 1/2 0.5 1.27 2/3 0.6666667 1.6933333 5/6 0.8333333 2.1166667
If we are dealing with sixths of an inch for typewriters, the next step is to be concerned with points as used by printers.
When dealing with a laser printer, or, for that matter, an IBM Selectric Composer, a point is exactly what it tends to be thought of as being nominally: 1/72nd of an inch, or 0.01388888...89 inches.
However, with printer's type, a point is slightly different: 0.013837 inches (or 0.03514598 centimeters). And Linotype machines work to a point which is 0.014 inches (or 0.03556 centimeters) in size. (This point is descended from the 0.0137 inch point of Fournier and the 0.0138 inch point of Nelson C. Hawks.)
In Continental Europe, a different type of point, the Didot point or Didone is used. Fourteen Didot points are very close to 15 points in height; a more precise figure is about 14.975 points.
Originally, the Didone was 1/72nd of the pre-Revolutionary inch, which in turn was 1/12 of the pied du Roi. As the French foot was originally 12.7892 inches in length, this works out to about 0.0148023 inches or 0.0375979 centimeters.
In 1879, Firmin Berthold revised the Didot point system to connect it with the metric system: a Didot point became 1/2660th of a metre, which is about 0.014800781 inches or 0.037593985 centimeters.
A metric Didot point of exactly 0.0375 centimeters has been proposed, and may in fact be in use, and the French Imprimerie Nationale is said to use a point of 0.04 centimeters. Also, it has been proposed to measure printing type directly in millimeters.
The second is defined as the time taken by 9,192,631,770 oscillations of the microwave radio frequency produced by an atom of Cesium-133 when the electrons in that atom are in the ground state, except for one that has emitted this radiation by making the transition from the upper hyperfine level of this state to the lower one. This definition was chosen to make the length of the SI second the same as that of a second of Ephemeris Time, based on the length of the day in 1900, and so when this second began to be used in civil timekeeping (the changeover to "atomic time"), the use of "leap-seconds" became necessary immediately.
At one time, the meter was defined as 1,650,763.73 wavelengths of the orange red line in the spectrum of Krypton-86 which corresponded to the radiation emitted by an electron moving from the orbital
2 p to the orbital 5 d 10 5
in an unperturbed fashion.
However, a scientist proceeded to measure the speed of light by performing an accurate measurement of the ratio between the wavelengths (and/or frequencies) of these two types of radiation. In Zen-like fashion, this convinced those responsible for the standards of the fundamental absurdity of the situation, and so now the definition of the second stands, but the definition of the meter has been replaced; now, the meter derives from the second, through the speed of light, which is, by definition,
8
2.99792458 * 10
meters per second.
Note that it is more convenient to measure the length of waves of light through interference fringes, and the time between oscillations of radio waves through electrical circuitry, however. So the dual definitions allowed both time and distance to be more accurately defined. Incidentally, as far back as 1927, a definition of the meter in terms of a light wavelength existed, but that definition was based on a line in the spectrum of cadmium.
It may also be noted that in 1964, an agreement was reached between the U.S. and Britain to define the inch as 2.54 centimeters.
Prior to 1964, the inch was defined in the U.S. on the basis that a meter was exactly 39.37 inches long, which led to the inch being about 2.540005 centimeters long, and in Britain the inch was 2.539997 centimeters in length.
The U.S. pound is defined as 453.5924277 grams, and the British pound is very nearly identical to it.
A pound is 7000 grains in weight, that is, the normal, 453.59 gram pound used to weigh food. Thus, if you have peas to weigh, you use this pound, which is called the avoirdupois pound. The troy ounce, which is used to weigh gold, however, is 480 grains in weight, and there are twelve troy ounces in a troy pound.
Prior to the devaluation of the U.S. dollar in 1933, which also led to the abolishment of gold coinage, the U.S. dollar was defined as the value of 258 grains of 9/10 fine gold. In U.S. coins, the remaining tenth was made up of half silver and half copper, which were not without value themselves.
People writing mediaeval role-playing games should note that due to the difference in density between gold and silver, if one uses the historic ratio that gold is 16 times more valuable than silver by weight, then it is also (approximately) 25 times more valuable than silver by volume. This will make it possible to determine more accurately how much treasure your characters can carry in their backpacks.
The density of gold is 19.32 grams per cubic centimeter, that of silver 10.5 grams/cc, that of copper 8.96 grams/cc. A ratio of 128:1 in value by weight would lead to a ratio of 150:1 in value by volume for silver and copper as metals. Copper coins tend, however, to be a token currency, that is, a metal form of paper money as it were, and so the ratio in weight of copper coin to silver coin would be more like 16:1 or 32:1.
The atomic weight of gold is 196.9665, and its one stable isotope is Gold-197. An atomic mass unit is
-24
1.6605655 * 10
grams.
Thus, one grain of gold is .064798918... grams of gold, and would contain some
20
1.9811592 * 10
atoms of gold.
Using a 16:1 ratio of value between gold and silver, and a 128:1 ratio of value between silver and copper for a 2048:1 ratio of value between gold and copper, one finds that U.S. gold coins have a metal content whose value is that of 258 * (.9 + .05/16 + .05/2048) = 233.0125488 grains of gold per dollar, one could, if one wished, define a dollar as the pecuniary value of
22
4.6163495 * 10
atoms of Gold-197.