Decimal precision

I believe you are confusing decimal precision ( number of digits to the right of the decimal point) with the number of significant figures. The two are not necessarily related. ________________________________________________________ Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)

Many years ago, before Windows, I wrote a program using "single precision" in GWbasic. The program would accept the input values (four decimal places) to produce a curve on the screen. Prior to this program, it took 4 hours to draw the curve. The program did it in less than 15 minutes including input time. The math included squaring numbers and getting square roots to determine the formula of the curve. With many pairs of input numbers, the program performed great. The problem occurred when just three (3) pairs of input data were entered. Then the curve was above the points or not on the screen at all. The problem was the "single precision" which was six significant figures. Changing the variables to "double precision" (17 significant figures) eliminated the problem. Format your input and output to display as many decimal places as practical for your needs (3, 4, 5,

6 decimals), but be certain the program can handle the accuracy of the math involved.

In my work, mechanical design of rolling mill machinery, 3 place decimals was adequate. If I were designing a watch, I may require more than 4 place decimals. They are ways to get around very accurate dimensions. One millimeter equals 1/25.4 inch or 0.039370078+ inch. The medical profession uses the metric system.

Good luck, Jim Y

From: Ed Ruf egruf snipped-for-privacy@cox.net

I'll add to that. Careful about deciding how many "digits" to keep at any step in your calculations. Just because you don't want too many in your final answer doesn't mean you should chop off digits in your intermediate calculations.

Also... the number of digits required is a function of what you are calculating and how accurate your answer "has" to be. Some applications require as exact of an answer as possible. Some don't. It is YOU who must decide what is appropriate. As such, there really is NO SUCH THING AS A "NORMAL" DECIMAL PRECISION. Be wary of any professor who tells you otherwise.

Dan :-)

Hi all,

Sorry about the confusion. I think I switched what I was thinking about between the the subject and the body.

I usually only leave for sig figs for the final answer. I was thinking that ten places should be good enough for most intermediate calculations. I understand I have to decide sig figs myself. Thanks for your input.

Thanks, Josef

In calculations, keep as many figures as is convenient and practical. Remember that a lot of engineering calculations involve some pretty hefty approximations anyway.

If you are trying to figure out how fast a horse runs, whether you use a number with three-digit precision or ten-digit precision for the horse's mass doesn't matter much, if the formula you're using assumes that the horse is a sphere.

There is an ASTM standard (E29) which deals with significant figures. I think it also contains some guidance on how many figures to use in calculations. If your school library has the annual book of ASTM standards, and you want the "final word" on this (or at least until the next set of ASTM standards comes out), you could look it up.

Dave Palmer

With modern calculators it really isn't much of an issue. Use all the digits you can get your hands on and then truncate what you don't need on the final result. The whole notion of "significant figures" stems from the days of slide rules and hand calculations, when being modest with your digits actually saved time. Any digits beyond four or five sig. figs. become immeasurable anyway.

Don Kansas City

SNIP

Actually the 3 sig figs of slide rule day came from the fact that most slide rules used for calculations could do no bettter than 3 sig figs.

Also how accurately are the properties used in the calcs known? moment of interia of the "real" section, area, modulus, yield stress, imposed loads?

3 sig figs gives an answer with % or better; more than good enough. Any attempt at a more "precise" answer is just wishful thinking.

cheer Bob

cheers Bob

The message from Don misses the point. The term "Significant Figures" really means what it says: How many figures are significant? How many figures (decimal places) really mean anything, and how many are just continued arithmetic? The whole idea is that we should not state results that are better than the data that they are based upon. If your input data is only known to three digits, then if is foolish to think that your finally calculated results are good to twelve places just because the computer printed them out that way.

There was more attention paid to this concept during the time when all calculations were done by slide rule because it was a matter of time economy. Today with computation by machine (or calculator) to many digits with ease this is no longer an issue, but the issue is still very real.

There are rules for determining the number of significant figures in a result, depending on the type of mathematical operations performed. It is quite possible to have three significant figures in the input data and have only one significant figure in the final result. Few people seem to be concious of this today, and perhaps that is where some of our difficulties come from.

Significant figures are significant!

The industry is the determining factor. If you are manufacturing watches then you may require several decimal places in your answers. If you are building bridges across rivers, I would think no decimal places are required, just a lot of shims.

In one industry, a tolerance of plus or minus 0.005 inch was the norm and we used three decimal places. In another industry, a tolerance of plus or minus 0.01 inch was the norm and we used two decimal places (and a lot of shims). I spent many years designing rolling mill machinery. One aluminum client used our mills to roll aluminum foil 0.000055 inch thin. That is 55 millionths of an inch. That is 6 decimal places but only 2 significant figures.

A computer program that uses many significant figures to acquire the answer can be used in many industries. The user just rounds off the answer to one that is normal for the industry in question.

Josef, I suggest you look at Chapter 34. Geometric Conformance, in the following text: "Tool and Manufacturing Engineers Handbook", Daniel B. Dallas, McGraw-Hill, ISBN

0-07-059558-5

Jim Y

snipped-for-privacy@gmail.com schrieb:

Here is a little problem to demonstrate that many places can indeed be necessary during computation - even though the input and result figures have no more than four places!

Compute the scalar product (dot product) of these two vectors:

x: [10^20, 1223, 10^24, 10^18, 3, -10^21];

y: [10^30, 2, -10^26, 10^22, 2111, 10^19];

The correct result is 8779. Good luck!

Hint: This sort of problem is "piece of cake" for Computer Algebra systems (like Macsyma, Derive, Mathematica, Maple or Mupad), since they work with arbitrary precision, i.e. as many places as necessary, if enough memory is available. An open source freeware System which does it is Maxima (O.s. version of Macsyma). You can get it at

Franz

That would be a big mistake. Unfortunately we human are so short sighted, all practical calculations depend on measurements and measurments depend on thier uncertainties (assuming special causes elimated..HAHa) - with a measurement you also get a variance - often ingnored. Do yourself a favor and read "An Introduction to Error Analysis" by John R Talyor before you waste your time.

Ed