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Significance arithmetic is a set of rules (sometimes called significant figure rules) for approximating the propagation of uncertainty in scientific or statistical calculations. These rules can be used to find the appropriate number of significant figures to use to represent the result of a calculation. If a calculation is done without analysis of the uncertainty involved, a result that is written with too many significant figures can be taken to imply a higher precision than is known, and a result that is written with too few significant figures results in an avoidable loss of precision. Understanding these rules requires a good understanding of the concept of significant and insignificant figures. The rules of significance arithmetic are an approximation based on statistical rules for dealing with probability distributions. See the article on propagation of uncertainty for these more advanced and precise rules. Significance arithmetic rules rely on the assumption that the number of significant figures in the operands gives accurate information about the uncertainty of the operands and hence the uncertainty of the result. For an alternative see interval arithmetic. An important caveat is that significant figures apply only to ''measured'' values. Values known to be exact should be ignored for determining the number of significant figures that belong in the result. Examples of such values include: * integer counts (e.g., the number of oranges in a bag) * definitions of one unit in terms of another (e.g. a minute is 60 seconds) * actual prices asked or offered, and quantities given in requirement specifications * legally defined conversions, such as international currency exchange * scalar operations, such as "tripling" or "halving" * mathematical constants, such as π and e Physical constants such as Avogadro's number, however, have a limited number of significant digits, because these constants are known to us only by measurement. On the other hand, c (speed of light) is exactly 299,792,458 m/s by definition. ==Multiplication and division using significance arithmetic== When multiplying or dividing numbers, the result is rounded to the ''number'' of significant figures in the factor with the least significant figures. Here, the ''quantity'' of significant figures in each of the factors is important—not the ''position'' of the significant figures. For instance, using significance arithmetic rules: *8 × 8 = 6 × 101 *8 × 8.0 = 6 × 101 *8.0 × 8.0 = 64 *8.02 × 8.02 = 64.3 *8 / 2.0 = 4 *8.6 /2.0012 = 4.3 *2 × 0.8 = 2 If, in the above, the numbers are assumed to be measurements (and therefore probably inexact) then "8" above represents an inexact measurement with only one significant digit. Therefore, the result of "8 × 8" is rounded to a result with only one significant digit, i.e., "6 × 101" instead of the unrounded "64" that one might expect. In many cases, the rounded result is less accurate than the non-rounded result; a measurement of "8" has an actual underlying quantity between 7.5 and 8.5. The true square would be in the range between 56.25 and 72.25. So 6 × 101 is the best one can give, as other possible answers give a false sense of accuracy. Further, the 6 × 101 is itself confusing (as it might be considered to imply 60 ±5, which is over-optimistic; more accurate would be 64 ±8). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Significance arithmetic」の詳細全文を読む スポンサード リンク
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