Quite some time ago, the [manufacturing] company for which I worked decided to do away with fractions in shop drawings. They had used 16'ths, 32'nds .. 128'ths. BUT, get this, they wouldn't allow (say) 0.25; it had to be 0.24 or 0.26 because that was the way scales were marked. The notion of interpolation was a no-no. Consequently, all sorts of troubles persisted; places where a quarter of an inch was really needed; cumulative discrepancies and so on. Duncan -----Original Message----- From: kilopascal <[EMAIL PROTECTED]> To: U.S. Metric Association <[EMAIL PROTECTED]> Date: February 12, 2002 00:25 Subject: [USMA:18162] Re: Weather reports during the Olympics
>2002-02-11 > >I can answer that from experience. First review USMA 18094. It seems >fractional use, as least in the US is restricted to halves, quarters, >eighths and sixteenths. Nothing more. It has to do with innumeracy. Even >an ignorant imbecile can divide something in half, in half again, in half >again, and in half again. After halving 4 times (16-ths), the person >doesn't have the feel for the numbers anymore. There is something about the >way people think that someone innumerate has a problem counting or doing >math with numbers bigger than 20 or smaller than 1/20-th. Thus they are >stuck in that range. That is why historically, unit conversions never >exceed 20:1. The innumerate of the old times could not manipulate the >numbers. > >When you hear about the use of fractions in FFU measurements, it means only >those sub-multiples of 1/2. Nothing else. And despite the years of math >time devoted to fractional manipulation, the average adult can not do any >better manipulating fractions then their innumerate ancestors. Just goes to >show you what a waste of time teaching fractions to the extent it is taught >today really is. > >I've heard it said that use of fractions or decimals in FFU engineering that >are sub-multiples of 1/2, are called LEGAL FRACTIONS. Fractions outside of >this sequence are illegal. In other words, only legal fractions may be >used, and illegal fractions and their decimal equivalents are to be avoided. >Thus 0.50 is legal, 0.49 or 0.51 is illegal. However, 0.31 is also legal, >as it is still considered 5/16. 3/8 can still be legally written as either >0.37 or 0.38, depending on the situation. But, 0.39 is illegal. > >The use of the term legal, is kind of a policing action to keep one from >drifting away from the "binary" fractions when using decimals. To me, this >limits the usefulness of inches and identifies the engineer who restricts >him/herself to binary fractions as being innumerate and subject to ridicule. > >John > > > >----- Original Message ----- >From: "Stephen Davis" <[EMAIL PROTECTED]> >To: "U.S. Metric Association" <[EMAIL PROTECTED]> >Sent: Monday, 2002-02-11 19:14 >Subject: [USMA:18156] Re: Weather reports during the Olympics > > >> Yes, I completely misunderstood the meaning of 'binary fractions', Joe!! >> >> Perhaps I am going to further compound my ignorance with this next >statement but, why does Marcus feel they would want a conversion to binary >fractions?? >> >> I for one am nonplussed by the need for anything but the decimal >equivalent of the metric amount, e:g, 2.54cm = 1 inch or 6.35cm =3.5 >inches!! >> >> Marcus also referred to measuring tape!! I would have thought if this >were to be graduated in fractions, they would be the ordinary ones, not >binary fractions!! >> >> Regards, >> >> Steve. >> [EMAIL PROTECTED] >> >> ----- Original Message ----- >> From: "Joseph B. Reid" <[EMAIL PROTECTED]> >> To: "U.S. Metric Association" <[EMAIL PROTECTED]> >> Sent: Monday, February 11, 2002 9:11 PM >> Subject: [USMA:18147] Re: Weather reports during the Olympics >> >> >> > Marcus wrote is USMA 17138 >> > >> > >Try getting a value of, say, 13.730 m into in-ft. The conversion in >> > >decimal is evidently straightforward (45.046 ft). But try now to get >the >> > >in thing in (0.55 in) stated as a binary fraction. For instance, 9/16, >> > >would be simplest fraction that would be the closest to that value, but >it >> > >"overshoots" it, 0.56 vs. 0.55, and stating it as simply 1/2 would err >by >> > >a whopping 1.3 mm! The best binary rounding would be 35/64, but how >many >> > >tapes nowadays would provide that accuracy? >> > > >> > >The challenge to program calculators to "make decisions" like this >would >> > >be overwhelming! That's why we haven't seen (to my knowledge) any >product >> > >in the market that would do this (yet...). And I sincerely hope we >never >> > >will!.. >> > >> > Stephen Davis replied in USMA 18142: >> > >> > >I see your point, Marcus, but surely a TV company (they certainly don't >do >> > >so over here, to my knowledge) would not bother converting metric to >> > >binary fractions anyway!! >> > > >> > >Surely the decimal equivalent would suffice?? >> > > >> > >Incidentally, unless I have missed your point by a couple of km, 0.55mm >> > >converted to a binary fraction would be 11/20, wouldn't it?? >> > >> > >> > >> > I quibble: 11/20 is not a binary fraction, although that is the vulgar >or >> > common fractional wquivalent for 0.55 that I get from my Casio fraction >> > calculator . A binary fraction fairly close to 0.55 is 563/1024. The >error >> > is only -0.000 195 312 5. >> > >> > >> > Joseph B.Reid >> > 17 Glebe Road West >> > Toronto M5P 1C8 TEL. 416-486-6071 >> > >> >
