Uncertainty in Measurements: Understanding Multiplication Factors

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Discussion Overview

The discussion revolves around understanding how to determine and record uncertainty in measurements, particularly in the context of using a digital voltmeter. Participants explore the application of multiplication factors for accuracy and the proper way to express uncertainty in recorded measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant asks how to know when to multiply calculated data values to determine uncertainty.
  • Another participant requests clarification by providing an example involving a digital voltmeter's accuracy and uncertainty specifications.
  • There is a discussion about how to record the reading of the voltmeter along with its uncertainty, with one participant suggesting to add the percentage of accuracy to the additional uncertainty.
  • Participants discuss the implications of rounding off uncertainty based on significant figures or decimal places, with some expressing confusion about which method to use.
  • A participant argues that significant figures are not practical in real-world applications and suggests following organizational reporting conventions instead.

Areas of Agreement / Disagreement

Participants express varying views on the proper approach to rounding and reporting uncertainty, with no clear consensus reached on whether to prioritize significant figures or decimal places.

Contextual Notes

Participants mention specific accuracy and uncertainty values from a digital voltmeter, but the discussion does not resolve how these should be universally applied or interpreted in different contexts.

Who May Find This Useful

This discussion may be useful for students or professionals dealing with measurement uncertainties in experimental physics or engineering, particularly those using digital voltmeters.

averycasille
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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?
 
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I have no idea what you are asking, Perhaps you could give an example of your issue.
 
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?
 
averycasille said:
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 )
 
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
 
averycasille said:
so, regarding the rounding off, that should be based on significant figures/decimal place of the data? O.O[/QUOTE

yes
 
gleem said:
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.
 
Thanks, peeps! But, significant figure OR decimal place? Sorry for asking a lot [emoji848][emoji23][emoji24]
 
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
 
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Thanks for the assistance, everyone. Means a lot [emoji120] Really appreciate it!
 

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