Am 2000-02-11 um 05:01 h (PST) hat Paul Keinanen geschrieben: > when making measurements, we are always talking about approximations > that are made at some precision. The number of significant digits in > a decimal number is a convenient way of giving an indication at what > precision the measurement has been made without explicitly specifying > the error limits. Agreed. A convenient way, but not the only conceivable one. On this ground, I want to comment on the following. Am 2000-02-11 um 05:01 h (PST) hat Paul Keinanen weiter geschrieben: > On the other hand a statement like "the length of the pole was > measured as 22/7 meters" [...] would indicate an exact entity No. Rather, this would indicate that the accuracy is not specified and must be separately elicited when needed. Again, the 3½" floppy disk is an example: here, 3½ is an approximation for 900/254. The only difference is that the implied accuracy in vulgar fractions is not as obvious as in decimal ones. It may be half a unit of the numerator, such that 3½ really means 3½ ± ¼ (in other words: 3¼..3¾). In many cases, the accuracy is meant to be much better; so, another interpretation of 3½ could be "closer to 3½ (or 7/2) than any other fraction expressable with one-figure nominator and denominator" -- with the obvious extension to finer precisions. When the fraction is always reduced to lowest terms (is this the correct technical term?), then any implicit indication of accuracy is lost (as with decimal fractions when trailing zeroes are removed). E. g., 4/8 carries a hint on its implied accuracy, while ½ may be meant to be accurate somwhere between absolutely accurate through ±¼. Am 2000-02-11 um 05:06 h (PST) hat Clive Hohberger geschrieben: > One should not overlook that vulgar fractions often express > quantities with absolute accuracy. Vulgar fractions are not intrinsically endowed with any more precision than decimal fractions are. In any case, you must specify the accuracy, in addition to the value. For example, you could specify the exact length of an inch either by a decimal fraction, viz. 2.54 cm, or by a vulgar fraction, viz. 254/100 cm. Cf. above for an example of a vulgar fraction meant to be inexact by over 1%. Am 2000-02-11 um 05:06 h (PST) hat Clive Hohberger weiter geschrieben: > For example, "7 1/3" is accurate, but that same accuracy cannot cannot > be attained in a decimal expression "7.333..." with a finite number of > digits. There are indeed rational numbers that cannot expressed exactly in a finite number of decimal places. However, every rational number can exactly be expressed with a periodic decimal fraction, where the period comprises a finite number of decimal digits. Best wishes, Otto Stolz