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Uncertainty significant digits 
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#1
Feb2714, 05:01 PM

P: 295

When dealing with the intermediate value of example: 570 +/ 100, how do you put this into it's final form? If I'm not mistaken, doesn't the uncertainty only contain 1 significant digit? Doesn't the uncertainty digit have to correspond to the final significant digit on the actual value as well? In that case, is the final answer 600 +/ 100 or is it appropriate to leave as 570 +/ 100 as the final answer?



#2
Feb2714, 06:53 PM

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Something more reasonable would be 570 ##\pm## 5. This suggests that there is uncertainty in the tens place (7 digit), but having 570 ##\pm## 100 suggests uncertainty in the hundreds place (5 digit), which makes the 7 digit worthless. 


#3
Feb2714, 10:20 PM

P: 295

Also, what happens if you have units in the exponent? Just curious, is it possible? 


#4
Mar314, 02:48 PM

P: 295

Uncertainty significant digits



#5
Mar314, 05:10 PM

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#6
Mar314, 10:26 PM

P: 295

I may have done an erroneous calculation and not cancelled units properly, but I'll try to find the example I was working on a while ago and post it if I find it. As long as there is no method to actually consider units in exponents in ordinary equations, that should be helpful enough since units most likely do cancel in the aforementioned problem. My last question is: why are some quantities vectors while others aren't? For example, we can calculate both current and current density, but why do we only consider current density to be a vector and current a scalar quantity? Is it a purely arbitrary convention or is it something more mathematically fundamental? I understand vectors like forces and displacement have directions and magnitudes associated with them, but I don't quite understand why we don't do the same thing for quantities like current? Is it to simplify equations only? 


#7
Mar414, 05:37 AM

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570 +/ 100 is a statement that the actual value lies between 470 and 670 with a certain probability. 600 +/ 100 is a statement that the actual value lies between 500 and 700 with the same probability, and that's a different thing. It made sense to use significant digits in intermediate values back when people used slide rules for intermediate calculations, so the method of computation itself introduced uncertainties that were directly related to the digit position. But that was then. 


#8
Mar414, 05:39 AM

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#9
Mar414, 02:27 PM

P: 295




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