John (Steele), Thanks for pointing out that:
1. the exact product of lbm and 9.80665 = (exactly) lbf (by definition of lbf) which is cited numerically on Page 53 of NIST SP 811 (2008 Edition) as Footnote 23, and that 2. computers capable of double-precision calculations can do the arithmetic directly without fracturing, and that 3. units *outside* SI (such as lbm and lbf) are often *defined* as exact multiples of an SI unit with a number of significant digits used for definition which is much larger than the number actually necessary to be retained after appropriate rounding, for most applications, and that 4. YES, it is best practice to store the exact definitions in memory to as many digits as storage fields permit, before calculations, and to do all appropriate rounding *after* calculations are done with the excess number of digits. On all these four points at least John and I are in complete agreement! I hope some readers will actually test the arithmetic of f = m a, and not merely accept the NIST product number (m a) without confirmation either by a double-precision calculation or by a single precision fractured calculation. I am curious to know haw many readers have actually or plan to work through the multiplication? Doing so will increase your appreciation of the gravity-free advantage of of SI! Eugene Mechtly ________________________________ From: John M. Steele [[email protected]] Sent: Friday, May 10, 2013 5:22 PM To: mechtly, eugene a; U.S. Metric Association Cc: mechtly, eugene a Subject: Re: [USMA:52755] Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law Well, 1) I didn't realize we were having a contest 2) The exact figure already appears as footnote 23 in Appendix B of NIST SP811 3) There are many calculator apps for PCs that use double precision floating point and can do the multiplication directly and explicitly (as can Excel) While it is more digits than would ever be needed, I do think it is useful to have "exact" values (or at least the full precision of the math processor) in computerized conversion routines. It makes little sense to store the "wrong" value when you can store the "right" value as a compiler constant. ________________________________ From: "mechtly, eugene a" <[email protected]> To: U.S. Metric Association <[email protected]> Cc: "mechtly, eugene a" <[email protected]> Sent: Fri, May 10, 2013 6:08:13 PM Subject: [USMA:52755] Numerical Verification of lbf and lbm with 9.80665 in Newton's Second Law Why has no person yet volunteered a confirmation of the exact arithmetic of lbf and lbm in f = m x 9.80665? Do the exact numerical values simply have two many necessary digits to be multiplied exactly by most of us? Hint: Use (a + b) x (c + d) where the numbers ( ) with "too many digits" are expressed as sums, and each part of each sum is initially expressed in exponential form. Then, this exercise becomes tractable on many inexpensive digital calculators. Who will be the first to confirm the exact fit of lbf and lbm (as *defined* numerically) with Newton's Second Law? Or, would most of you simply prefer to trash all that is non-SI? (a perfectly respectable attitude) Eugene Mechtly
