DECIMAL DUST – I love it. In my over 40 years of being involved in science and science education, I’ve never heard this one, and wish I had, because I would have used it over and over again, in describing the decimal noise that proliferates among both students and other folks who don’t know what they are doing when it comes to the use of significant digits [e.g. the 10 places that a calculator produces appears as an answer on a test when perhaps no more that 3 make any sense].<2005 “And congress budgeted only $150 million or so for financial aid [[to nursing students]], with the result that 82 percent of federal-loan applicants were rejected. ‘The public sector needs to take this on ,’ says Peter Buerhaus, a health economist at Vanderbilt University. ‘We’re talking DECIMAL DUST compared to the billions spent in Washington.”—‘Newsweek,’ 12 December, page 80>
In physics we try to teach the basic rules of measurement and the propagation of errors in calculations using these measurements, and accuracy, precision, and significant digits are important topics. To ascertain the propagation of errors accurately one must employ differential calculus. However, for such simple operations as addition, subtraction, multiplication, division, squaring, and square roots the rules are simple and don’t have to be rederived every time.
After Kennedy (in 1962) challenged the nation to put a man on the moon by the end of the decade, I actually spent about six months of my life, on my first job out of college (1963), working on this sort of thing using the feedback control system equations of our early inertial guidance systems – the systems that tell a spacecraft where it is and guides it to its final destination. My task, at the company I was working for, was to develop the equations that would be used to calculate the errors incurred in position, velocity, acceleration, etc. due to various inaccuracies in the guidance system – which, miraculously (for me at least – using a pencil, a piece of paper, and a slide rule in lieu of the not-yet-available digital computer), I actually accomplished! Heading the project at my company was a recent defector from Russia, a rocket scientist, who brought many of their guidance secrets with him. Ah, the ‘space race.’ Those were heady times! But I digress.
Since DECIMAL DUST, as I see it, is all around us – an extremely apt expression, not only for an insignificant amount of money but also for general decimal noise, I figured that I ought to find out where it came from, how long it has been around, etc. None of my usual sources listed it, but a Google search produced 1875 hits – a not insignificant number – and with the very first hit on the list I hit pay dirt. WordSpy.com had addressed the question:
DECIMAL DUST: An inconsequential numerical amount.
Example Citation: “In 1999, Gonzalez received $1.4 million from the National Institutes of Health to compare his enzyme-nutritional therapy with the best chemotherapy now available for the treatment of advanced pancreatic cancer. As a percentage of the fifteen billion dollars that the federal government spends on medical research annually, the grant amounts to what one federal health official described to me as ‘decimal dust.’”—Michael Specter, "The Outlaw Doctor," The New Yorker, February 5, 2001
Earliest Citation: “Critics worry that as partnerships bloom, they could drain billions of tax dollars from the Treasury, and even lead to the ‘disincorporation’ of America. The Treasury Department originally estimated it could raise $665 million over a five-year span by changing the tax status. The Stanger Report dismisses that revenue estimate as exaggerated, saying revised Treasury studies now say the government would gain just $24 million next year if it taxes MLPs as corporations — ‘decimal dust,’ as one senator put it."—Stephen Maita, ‘The Bloom is Off the MLP Market,’ The San Francisco Chronicle, July 27, 1987.
Notes: Something (usually a dollar amount) gets called decimal dust after it has been compared to something much larger. For example, consider the numbers in the citation above: Dividing the $1.4 million received by the doctor with the $15 billion medical research budget, the result is 0.000093. That tiny decimal fraction makes the smaller monetary amount seem almost nonexistent, as though it could be blown away like a speck of dust.
But, for my personal use, I will further define it as not only being 'an inconsequential numerical amount' but also a ‘fallacious numerical amount,' those extra meaningless digits – that decimal noise – based on the improper use of significant digits in calculations. The truth ain’t just what your calculator happens to spit out!
Ken G – December 8, 2005<1992 “Researchers at AEA Technology’s Harwell Laboratory in Britain recently turned a Cray-2 supercomputer loose for 19 hours. The result: an new ‘largest’ prime that leaves the previous record-holder trailing in its DECIMAL DUST.”—‘Science,’ New Series, Vol.256, No. 5054, April, page 175>
<2003 “And when I started to chase this down, I talked to somebody on the Interagency Council for Homelessness at the White House, and he said to me, hey, Jack, this is DECIMAL DUST [[the $600,000 needed for a rejected homelessness program]] okay?”—‘U.S. House of Representatives Hearing on Veterans Affairs, 6, May>
<2005 “The differences in average scores between [[assessment test series numbers ]] 7 & 8, and 9 & 10 amounts to ‘DECIMAL DUST.’—Assessment Newsletter,’ Owens Community College (Ohio), Spring>