Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site rtech.UUCP Path: utzoo!linus!philabs!cmcl2!seismo!lll-crg!dual!unisoft!mtxinu!rtech!jeff From: jeff@rtech.UUCP (Jeff Lichtman) Newsgroups: net.med Subject: Re: The Perils of Nutrasweet: digits of precision Message-ID: <587@rtech.UUCP> Date: Thu, 8-Aug-85 02:54:18 EDT Article-I.D.: rtech.587 Posted: Thu Aug 8 02:54:18 1985 Date-Received: Wed, 14-Aug-85 02:39:21 EDT References: <771@burl.UUCP> <394@petrus.UUCP> <182@steinmetz.UUCP> Organization: Relational Technology, Alameda CA Lines: 46 > In article <1634@orca.UUCP> andrew@orca.UUCP (Andrew Klossner) writes: > >>> I am positive that more than .007% ... > >> > >> 3-digit precision based solely on anecdotal evidence? > > > >Both the quoted numbers (.007% and 10%) have only one significant > >digit. Leading and trailing zeroes are not significant. > > I agree. 10% has only one significant digit, but .007% has three. The > decimal point makes the two leading zeros significant (i.e.: the original > article claims accuracy to three decimal places). > > The Polymath (aka: Jerry Hollombe) The usual method of writing numbers (e.g. 10, .007) carries no information about accuracy. .007 could be accurate to one, two or three decimal places. The only way to express accuracy is to put the number in scientific notation, or to explicitly specify the accuracy of the number. In scientific notation, 7 * 10 ** -3 has one digit of accuracy, 7.0 * 10 ** -3 has two digits of accuracy, and 7.00 * 10 ** -3 has three digits of accuracy. This method of notation makes incidental zeros impossible. If you saw 1000000, how would you tell which of the zeros were part of the measurement, and which were padding? 1.00 * 10 ** 6 leaves no question that there are three significant digits. This and the fact that scientific notation allows huge numbers to be written compactly are the two main advantages of this method of expressing numbers. However, one should remember that the accuracy of real measurements doesn't often conform to the decimal system of expressing numbers. That is, real measurements are not usually accurate within some integral number of digits. The number of significant digits in a measurement usually only gives a rough idea of the accuracy of the measurement; a better method is to give some measure of accuracy along with the measurement, such as standard deviation or range of 95% confidence (e.g. 7.00 * 10 ** -3 +/- 2.5 * 10 ** -4 with 95% confidence). Figuring this out can take a bit of calculus if the number in question is calculated from several variables, each with its own accuracy: one must factor in not only the accuracy of each of the variables, but also the sensitivity of the derived measurement to changes in each of the raw measurements. -- Jeff Lichtman at rtech (Relational Technology, Inc.) aka Swazoo Koolak {amdahl, sun}!rtech!jeff {ucbvax, decvax}!mtxinu!rtech!jeff