Uncertainty in Measurements: Understanding Multiplication Factors

[averycasille]

Hello, guys! (And girls, but.. you know..)
There are several things I do not quite understand, so, can you help me clear my doubts? ^^

1) How do I know when to multiply the value of calculated data when it comes to determining the uncertainty of the data?

2) When do I multiply the percentage of accuracy with given data when determining uncertainty?

 

[gleem]

I have no idea what you are asking, Perhaps you could give an example of your issue.

 

[averycasille]

Sorry for being unclear!
• The manufacturers of a digital voltmeter give, as its specification, accuracy +-1% with an additional uncertainty of +-10mV. The meter reads 4.072V. How should this reading be recorded, together with its uncertainty?

 

[gleem]

How should this reading be recorded, together with its uncertainty?

You record the reading as is 4.072 V. The uncertainty should be 1% of that reading + 10 mV.= 0.0407 V + .01 V = .0.0417 V =0.042 V ( rounding )

 

[averycasille]

Ohh. So, when the specific accuracy is given, I should always multiply with the data and add it with the additional uncertainty? Is that it?
Also, regarding the rounding off, that should be based on significant figures/decimal place of the data? O.O

 

[gleem]

so, regarding the rounding off, that should be based on significant figures/decimal place of the data? O.O[/QUOTE

yes

 

[jbriggs444]

You record the reading as is 4.072 V. The uncertainty should be 1% of that reading + 10 mV.= 0.0407 V + .01 V = .0.0417 V =0.042 V ( rounding )

0.0407V + 0.010 V = 0.0507V which is 0.051 after rounding to an appropriate precision.

 

[averycasille]

Thanks, peeps! But, significant figure OR decimal place? Sorry for asking a lot [emoji848][emoji23][emoji24]

 

[jbriggs444]

As a general rule, significant figures are not appropriate in the real world. They are a toy for the classroom. The reporting conventions for your organization should be followed. One recommendation from http://web.mit.edu/fluids-modules/www/exper_techniques/1.Recording.Uncertainty.pdf is:

"As described above, to determine a quantity x, we make a measurement, report our best estimate, and report the range over which we are reasonably confidant the actual value lies: (measured value of x) = xbest ± δx ."

e.g. 4.072 ± .051 V

 

[averycasille]

Thanks for the assistance, everyone. Means a lot [emoji120] Really appreciate it!