I hasten to add to my comments this morning that I recognize the importance of ratios, but, gee, gosh, and golly, I prefer to MEASURE DECIMALLY! So, on that point, Philip, I agree with you. But, I just don't think that ratios should be demoted to the rank that we metricationists have been assigning lately. Somewhere, even in the metric literature, I read the remark, "People will always cut things in half." I, too, am guilty of cutting things in half (grin).
----- Original Message ----- From: "Philip S Hall" <[EMAIL PROTECTED]> To: "U.S. Metric Association" <[email protected]> Sent: Sunday, October 16, 2005 09:59 Subject: [USMA:34904] Re: Approximations (was fractions) > > You choose the number of useful digits by knowledge of the situation. A > > person who is properly taught how to apply the rules of significant digits > > knows how many digits apply. A number left in fractional form is not an > > answer. If I have a number like 2/3, what does that mean if I'm trying to > > build something with it? > > 2/3 is no less an anwer than 0.67 > > Admittedly the problem presented is purely numerical with no context. > > > Even if you have a number such as 2/3, you still have to assign a level of > > accuracy to it. There is no way you can make something exactly 2/3 of > > something. You are always going to have to state a plus/minus something > > else. > > Alright, but it may not be an end result. It could be an intermediate step > involving a fractional coeifficient. Take as an example the formulae for the > volume of a sphere - 4/3 * pi * r^3 > > In any case, if the figure of 2/3 was an approximation for something, with a > known error bound, then by substituting a decimal approximation you > introduce a further error. > > Phil Hall > >
