A good question, to which I can't give a good answer. Much of it is notes and markups of documents that go back years, but it is rarely more than a few minutes on each observation, then record it. (It does require at least double precision math, not a ten digit calculator.) I probably spent a couple of hours on the letter and thinking about the idea that an "exact" number is useful as a definition even if it requires an impractical number of significant figures. Not everybody accepts that idea, but if you do, essentially every conversion (except those involving pi or e) can be stated exactly in decimal, or as a ratio of integers.
Those extra digits of precision are not really useful if you are keying by hand into a calculator, but they are useful as compiler constants in computer programs. If every constant is expressed as a 53 bit significand in floating point (about 15.9 digits), why use a wrong value when you can use a right value? Even in a metric world, there will be a lot of old data that will need to be understood. It is important to know how to convert from Customary (or Imperial) to metric. It is NOT important and perhaps undesirable to know how to do the reverse. However, except to idiots, it will be obvious you divide instead of multiply. :) Obviously, real world conversion requires understanding the precision of your input data, even if you use max. accuracy conversion constants. ________________________________ From: John Frewen-Lord <[email protected]> To: U.S. Metric Association <[email protected]> Sent: Thu, November 18, 2010 12:21:00 PM Subject: [USMA:48884] Re: NIST Handbook 44, Appendix C John, how long did it take you to work out and write all this stuff? A fair bit of time I would wager. None of this would be necessary in a metric only world. Gives some indication of the lost productivity experienced by the US (and to some extent the UK) on a daily basis by having all these conversion factors, not only between metric and non-metric, but between different units in non-metric measures. John F-L ----- Original Message ----- >From: John M. Steele >To: U.S. Metric Association >Sent: Thursday, November 18, 2010 5:05 PM >Subject: [USMA:48883] NIST Handbook 44, Appendix C > > >NIST Handbook 44, Appendix C is a great compendium of information >inter-relating >Customary, Imperial, and metric measure. However, the 5 subsections can be a >little confusing as conversions are stated to different precisions, in >different >sections. A recent comment by Pat on confusion of exact vs approximate values >caused me to look closer. Section 4 is probably the best source of exact >conversions. However, some are not correctly marked as exact or not, and in >several cases the exact value can be deduced, but is not explicitly stated. > >As a result of my review, I have submitted the comments below to the NIST >Weights & Measures office: > >Comments on NIST Handbook 44, Appendix C, 2010 Edition > >Handbook 44, Appendix C is an extremely useful resource for defining U.S. >Customary measure and its relation to the metric system. The data provided >has >more than sufficient accuracy for any practical purposes. However, I believe >a >few errors exist in the use of underlining to denote exactness. Further, I >offer a few suggestions for possible improvement. All comments relate to >section 4 of Appendix C; however, I have relied on some of the other sections >to >define exactness in my reasoning. I did not do a methodical review of prior >versions, but these comments generally apply to prior editions as well. > >Those figures which are underlined are intended to be exact, and may therefore >serve as definitional. I believe the following issues exist: > >1) In the first table of length - International, the figures 12 in/ft, 36 >in/yd, >1 ft/ft, 3 ft/yd and 1 yd/yd are not underlined, but are exact. Underlining >should be added. > >2) In units of capacity - liquid volume measures, it is not possible to state >exactly the volume of the minim decimally in terms of drams, ounces, or gills >(there is a division by three), yet they are underlined. Underlining should >be >omitted. Note: The exact value of the minim can be stated as 0.003 759 765 >625 >in³ if desired. > >3) In the cubic inch column of this table, the figures 1728 in³/ft³ and 1 >in³/in³ are not underlined, and should be. The value of 0.225 585 94 >in³/fluid >dram is marked as exact, but is not. The underline should be deleted, or the >exact value stated and underlined, > >0.225 585 937 5 in³/fluid dram (this value can be calculated from other >entries >in the table.) I recommend the exact value for completeness. > >4) In the first table of Units of Volume, exact definitions of the cubic inch >and cubic foot in liters are given and underlined. However, these figures are >rounded (and not underlined) in the dry and liquid measure tables. The use of >two different values is somewhat distracting and confusing. I recommend the >exact values be used in the dry and liquid measure tables (also in the >milliliter column of these tables). > >I have some additional suggestions for exact values. They will involve more >significant figures than could ever matter in practical measurement. However, >they aid in the rigorous definition of US Customary measure in metric terms >and >I urge their consideration: > >5) Since the release of a new datum (NAD83) and related geodetic data, USGS >has >allowed States to pass legislation and receive their geodetic data in meters, >International feet, or Survey feet, according to their preference. This >results >in a mess; however, some States have adopted the International foot. As a >result, I believe the table for units of area - International measure requires >the addition of an International acre, 4046.856 4224 m², exactly, based on >43560 >International square feet. The link, chain, rod, furlong, and related areas >are >perhaps sufficiently obsolete as to not require "international" definition. >Note: This issue may also indicate a need for some rewrite of NIST SP811, >Appendix B.6. > >6) The gallon and bushel are defined as 231 in³ and 2150.42 in³ respectively. >By multiplying these values by (0.254 dm/in)³, it is possible to give exact >values in liters for these quantities, as 3.785 411 784 L, and 35.239 070 166 >88 >L. The first requires no more decimal places than the values for cubic inch >and >cubic foot, already given, the value for bushel requires two more. Starting >from these values, each submultiple may also be stated exactly and decimally, >if >desired. > >
