Accuracy in calculations?

these work for me:

http://www.astm.org/Standards/E29.htm

http://www.astm.org/Standards/D6026.htm

The use of the sample standard deviation (1 sigma)to represent a confidence interval (given sufficient samples from a population) is another approach (if normal distribution).

milo

meaure tolorance belongs to normal distibution. so its max error would be less than 3sigma.

Approximate calculation is a subject.

significant figure is very useful at determinate result figure. but if you hope to know a process accuracy, you hve to use ways of approximate calculation. for your example of trangular function, say calculate a sin function, you will spread it into a series. for example, Tailor series, its residual terms will present you with the accuracy you wanted.(use e this complex number)

antoher example, differential can simplize a curve calculation. suppose, Y = x ²; at 2 neiboor, you can get deltaY = 2 X * deltaX ; say 2.1 you can get, 4+0.4=4.4 if you hope more accuracy, you spread 2 order or 3 order ... terms, so that you can approach original value infinitely. if you determine the accuracy in advance, you will use the residual terms of the series to determine how much terms you will use.

Please would one shorten the honerable 2 years of engineering language to how I just limit heat load studies to answers of only 3 sig fig's in engineering 102 terms , when you have a moment, as I know a little trig and differentials but never use in HVAC thermal transfer on calculations on the surface of numbers and multiplication... with addition but requiring a certain amount of accuracy...

Yes great work but I had the impression the thread poster wanted less than a bark park model with control of flexibility.

What is [ a bark park model with control of flexibility.]?

its out of my depth.

thanks.

It entirely depends on what you are calculating.

A go-no go gage or standard then? What discipline?

TVP45,

the old significant figure rule that we learned in the second grade isn't worth two hoots when doing trig functions,

Why not? Inverting the argument should be your tool...

Explain that, please. Am I overlooking something simple?

Yes actually.

Guest explains it quite well in post #9.

I am not Guest and thank you Guest

Im sorry in advance, I dont know if I can type here this words?

#9's answer is right, but not quite well ! Look at my answer above, you will know why he is not quite well.

He answered how the one order approximate way to take, but he hasnt answered the what accurancy.

Its pity you havnt yet found the issue. and select GA once more.

multi elements function is more complex operation to get its accurancy.

Hi tv45,

Suppose you have an equation x=a*sin(b)-c, and you know the errors for INDEPENDENT variables a, b and c to be ea, eb and ec.

If ea, eb and ec are sufficiently small, then you can estimate the error ex by differentiating the expression for x, i.e.:

ex=ea*sin(b)+a*cos(b)*eb-ec

If you estimate/ know the MAX absolute errors for a, b and c to be Ea, Eb and Ec, then the absolute worst case scenario for ex is:

Ex=sqrt((Ea*sin(b))^2+(a*cos(b)*Eb)^2+(-Ec)^2)

This is a pessimistic and (in case of gross non-linearities) rather crude, approximation, just like you asked for.

(The good news is that you can vary Ea, Eb and Ec for different confidence levels and thereby get a statistical-ish distribution for ex...)

There is your answer. Frankly, if you are dealing with complex clusters of variables, i.e. x=a*sqrt(b+sin(c)) etc, differentiating analytically gets VERY complicated, and becomes inadvisable. Your best bet then is actually the min-max, which will prove less cumbersome if you put all your calculations in an excel sheet and calculate for a myriad of possible random values (in less than a sec...). You do have excel, I hope.

Hope this helps!

GA, but log in to receive a rate

To enhance my previous post, and at risk of guilding the lilly somewhat and possibly exceeding my usual Brevquot.

Say you are playing golf and 100 yards from the green (you've paced it from the 150yd marker) however you have also paced that you are 30 yards left of the fairway centre...now Pythagoras' Law could give you the distance to the flag
X= √ (100² + 30²⁾ now this equals about 105 yards (half a club) you certainly don't need any decimals or even an accurate square root.

But remember to keep your head down, and try and stay on the fairway next time

Del

I hope you don't expect me to take accuracy advice from someone who whiffs the tee shot twice, goes into the rough where he takes three mulligans, finally just kicking the ball when nobody's looking, throws his 7 iron into the water hazard, nine putts, and then takes a 4 for the hole claiming spectator interference because a groundskeeper hit the ball with his head!

There is a formula you always can use,is different than a diferential and commonly more adjusted value:If y=f(x1,x2,---,xn),so then you estimate "y error" by:

{[(df/dx1)dx1]**2+------+[(df/dxn)dxn]**2}**(1/2)

Is understood dx1,---,dxn are not known values:are estimation of the most probable mistake of those variables,think it was "sigma" called.-

Just be thankful that we no longer have to do it with a slide rule...

Bill

Actually, the slide rule automatically limited your calculations to 3 (or 4 if you were really good and/or had a larger than standard slide rule) digits.

The simple answer is that the solution to a problem should be rounded to the number of significant figures from the least precise value, but what about the intermediate steps?

In 1995 my High School Chemistry teacher expected students to use a scientific calculator such as a TI-32 and insisted that students should always write down all values from intermediate steps rounded to the fifth decimal place (including values from sin(x), cos(x), etc.).

In 2003 my College Physics professor expected students to use a graphing calculator such as a TI-83 and insisted that students should achieve the highest possible precision using their calculators by never rounding off anything in intermediate calculations. (No one liked my Physics professor.)

The above can be achieved using a graphing calculator by reducing the equation as much as possible by hand using only variables then entering the reduced equation into the calculator in one step. If the equation is too complex to solve in one step, then intermediate values can be saved as variables in the calculator's memory which rounds the value(s) to the maximum number of digits that the calculator can store which is more than the calculator will show on the screen. This method is kind of the computerized version of the "slide-ruler rules" that some other members describe in this thread.

Finally, when all the hard work is done the answer is presented with the number of significant figures from the least precise value. Which is kind of nauseating in a classroom environment because the end result is that you have to keep up with 32 - 64 significant figures (depending on your calculator) in order to arrive at what is usually a 3 significant figure solution.

I agree with the concept of keeping a couple of extra digits to avoid rounding errors in intermediate calculations, then rounding the final answer.

Keeping and writing down all the digits a calculator can produce is ridiculous, even for intermediate calculations. (This is from an ex college and high school physics teacher, who did require students to show how they got their answers.)

I never suggested that anyone should write anything down. The desciption above says to either let the calculator perform the calculation in one step or to save intermediate values in the calculator (STO->Z).

If you use say an HP calculator it will tell you in the manual.