NO! becasue 1000 is the same as 0. Er - that needs explaining! i.e. there are 500 numbers 0-499 inclusive and 500 numbers 500-999 inclusive. So the 1000 is the 0 in the next set. Regards, Kevin ----- Original Message ----- From: "David W. Gulley" To: Sent: Thursday, May 31, 2001 3:30 PM Subject: Re: [OT]: Brain Burp Rounding?? > Roman Black wrote: > > > > Hi Michael, yep, darn right, half the people in > > the world (including me!) have been rounding wrongly > > their entire lives. Very scary. There is and can only > > be one correct way of rounding decimal numbers... > > > > Here is an example, assuming rounding to 3 decimal > > places, that is 1000 combinations, from 000 to 999. > > > > 000 to 499 (first half), 500 to 999 (second half). > > There are the first 500 combinations in the first > > half, and the second 500 combination in the second > > half. > > > > All my life I have been rounding at 555, under the > > false impression that 5 is "half way" in decimal > > terms... Wow. > > > > I asked my 26 yr old science-degreed girlfriend how > > to round and she looked at me like I was stupid. > > "5 or more, round up". She was taught correctly. > > > > Now I'm wondering if it is mainly us old-timers > > from the dawn of pocket calculators age that were > > taught wrong?? Any thoughts, older people?? > > :o) > > -Roman > > Cept for one minor detail, > > There are 999 values BETWEEN 0 and 1000. > 500 IS the halfway point. > 500 values below it (0 - 499) and > 500 values above it (501 - 1000). > Therefore, if accumulating a large series of "random" numbers and > rounding using the 5 or greater rule, the result will "tend" to be too > large since statistically you are using 500 possibilities below the > number and 499 above the number. > > For most things this error would probably not be a problem, but the > "round to even if 5" rule will "tend" to average out the error > accumulation at the expense of complicating the rule slightly. > > The validity of the least significant digits does play an important role > in the process, so when absolute accuracy is required use a tolerance > (+/-) to exactly specify the values, and the error accumulation. > For example (round to nearest 1/100): > Value Tolerance Round >=5 Round to Even if 5 > 1.125 +/- 0.005 1.13 1.12 > 1.135 +/- 0.005 1.14 1.14 > Repeat above 1000 times and Total > 2260 2270 2260 > > when the tolerances say: > 2260 +/- 10 or somewhere in the range of 2250 to 2270 so yes the > "Round >=5" is a 'correct' answer (since it is in the possible range > defined by the tolerances, even if it is at the upper limit), but the > 2260 provided by the "Round to even if 5" is a 'better' answer (in some > cases). > > Obviously this is a contrived scenerio, but if a particular sensor > reported to 0.5 units of precision with +/- 0.5 units of accuracy, and > you wanted to accumulate readings over a long interval, the "Round >=5" > will provide an answer that is "typically" too large. > > If you were buying gasoline, and the pumps all rounded using the "Round > >=5" rule, would you mind that you were charged for 2270 gallons instead of 2260? :-) > > As I stated in an earlier message in this thread, > This is a very debatable subject! > > > David W. Gulley > Destiny Designs > > -- > http://www.piclist.com hint: To leave the PICList > mailto:piclist-unsubscribe-request@mitvma.mit.edu > > > -- http://www.piclist.com hint: To leave the PICList mailto:piclist-unsubscribe-request@mitvma.mit.edu