Depends on how much tolerance, or how much accuracy, you want. 0.5 is less accurate than 0.500 which is less accurate than 0.50000000000.
This may make a difference when you are manufacturing something to very tight tolerances. Carleton -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Daniel Sent: Sunday, October 16, 2005 12:17 To: U.S. Metric Association Subject: [USMA:34908] Re: Approximations (was fractions) In your example of the volume of the sphere you are confusing a fractional number with three constants in an algebraic expression. Write it differently and the fraction isn't so obvious. Like 4 * π * (r^3) /3. The 4, the 3 and π are constants and r is the variable. You can manipulate the solution any way and then round the result. If r is 3, the r^3 is 27. 27 divided by 3 is 9. 9 times 4 is 36. 36 times π is 113.097 335 5 (As far as the calculator displays) . You can round this result to whatever significant digits are necessary. Would you leave the result as 36π because you don't want to see an irrational result? When performing a calculation, you leave all of your constants in their basic form, perform the calculation to the decimal result, apply the rule of significant figures and that is your answer. You don't leave a number in a fractional form, as in truth, a fraction is a step of division not completed. Why don't I write the number 4 in a result as 12/3? So why would I want to leave the number 0.5 as 1/2? Even whole numbers have significant figures. Is 1/2 always 0.5? Or can it also be 0.500000 or 0.500000000000? Where do the number of zeros really end? In reality a number like 1/2 is just as irrational as 2/3, but we consider the zeros to be of no value so we drop them. But, are they? In the world of number theory the zeros may not be of value, but in the world of manufacturing, they may be. Dan ----- Original Message ----- From: "Philip S Hall" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>; "U.S. Metric Association" <[email protected]> Sent: Sunday, 2005-10-16 10:59 Subject: Re: [USMA:34902] 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 > > > > -- > No virus found in this incoming message. > Checked by AVG Anti-Virus. > Version: 7.0.344 / Virus Database: 267.12.1/136 - Release Date: 2005-10-15 > >
