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 > > >
