Significant figures. A math problem.

(You guys help me with suspension questions for an MR2 and best methods to make a grilled cheese, so why not?)

I have calibration standards that I label with the thickness of the alloy coating, and the precentage of the alloy. For example, Zinc-Nickel over Steel 186 microinches 87% Zn.

My dilema is I'm trying to decide the significant figures to list for the alloy. How much more accurate is 86.6% versus 87%? The XRF (Xray Fluoresence) gauge spits out 86.62% but I think I can select the digits for the output, so not exactly the limiting factor.

I did some Googling yesterday and everything talked about figuring out what the significant figures are, vs how many to list. Any math geeks out there?

And here I thought we were discussing plus-size lingerie models.

But seriously, I'm not sure you've given enough information. What's the actual percentage? What's the tolerance? Who's going to see the numbers and will they care?

How precise is the XRF? That is, what are the specs? You could report whatever the precision of that machine is, in my non-professional opinion.

i've dealt with sig figs in labs some but it's been a while. I think in this case the actual measurement tolerances of the equipment determine your significant figures unless you are doing some kind of calculations after the fact. How you report them has more to do with the audience than the actual machine, though. Including the tolerance (+/-) on the machine is usually appropriate as well.

ultraclyde wrote: i've dealt with sig figs in labs some but it's been a while. I think in this case the actual measurement tolerances of the equipment determine your significant figures unless you are doing some kind of calculations after the fact. How you report them has more to do with the audience than the actual machine, though. Including the tolerance (+/-) on the machine is usually appropriate as well.

This!

We need to know the tolerances here.

If you're building a shed, it doesn't matter at all. If you're building a spaceship, you bet your ass it does matter.

As a applications engineer/machinist (not in a lab!), even though I understand tolerances perfectly fine, I also understand that the guy buying the machine/part wants to see wants to see the machine set up to cut this part @ +-.0001", even though this feature has a +-.005" tolerance. Hell, I had people specifically request that we make their rotary output display 4 digits! There is no way the encoders were accurate to .0001°, especially as they were cutting 6" away from center!

I'll echo what UltraClyde said above, I'd print whatever the machine is certified to output.

I can try to explain it simply...

If the best measurement accuracy you have is down to .1, you should not trust any digits further to the right of the decimal place.

when having 2 different accuracies from 2 different measurements is gets a little bit more complicated.

If I wanted to know the percentage of thickness from a coating versus the overall thickness of a part, my significant digits are reported based on the LESS accurate device.

For example:

Overall thickness I can measure is 1.1 mm. The thickness of the coating is .01mm.

I can only report the percentage to the .X decimal place.

When this can really become as issue is when converting units from SAE to metric. For example... 1 inch is NOT 25.4mm. It would be 25mm.

However, 1.0 inches IS 25.4 mm.

How about 1.0000 inches? Well, for that you would use the conversion factor of .0394 and get 25.37081. However, you could only report 25.3708.... And so on....

Your question falls right into my wheelhouse but I’m on a business trip doing my wheelhouse thing at the moment…I may have time tomorrow to help you out if you can wait.

wvumtnbkr wrote: I can try to explain it simply... If the best measurement accuracy you have is down to .1, you should not trust any digits further to the right of the decimal place. when having 2 different accuracies from 2 different measurements is gets a little bit more complicated. If I wanted to know the percentage of thickness from a coating versus the overall thickness of a part, my significant digits are reported based on the LESS accurate device. For example: Overall thickness I can measure is 1.1 mm. The thickness of the coating is .01mm. I can only report the percentage to the .X decimal place. When this can really become as issue is when converting units from SAE to metric. For example... 1 inch is NOT 25.4mm. It would be 25mm. However, 1.0 inches IS 25.4 mm. How about 1.0000 inches? Well, for that you would use the conversion factor of .0394 and get 25.37081. However, you could only report 25.3708.... And so on....

yup, much like that. great explanation.