Are these two masses considered equal up to the third digit?

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Homework Help Overview

The discussion revolves around the comparison of two measured masses, m1 and m2, with values of 0.552 kg and 0.556 kg, respectively. The original poster seeks to determine if it is appropriate to state that these masses are equal up to the third digit.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of measuring accuracy and the implications of percent difference in the context of mass comparison. There is a discussion about the validity of stating equality based on significant figures versus actual measurement accuracy.

Discussion Status

Some participants have suggested performing error analysis to determine if the masses can be considered equal within a certain percentage. Others have questioned the origin of the mass values and their implications for accuracy. The conversation is ongoing, with various interpretations being explored.

Contextual Notes

There is mention of one system having more data points, which may affect the reliability of the measurements. Additionally, the masses are described as potentially representing realistic systems rather than actual experimental results.

Niles
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Homework Statement


Hi

Say I have measured the mass of 2 particles, and I find

m1=0.552 kg
m2=0.556 kg.

I would like to say that the masses are equal up to 0.55. Is it proper to say "they are equal up to the third digit"?


Niles.
 
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It would be more proper to find the percent difference, x. If your measurement is accurate to a number greater than x percent, then you can say "The masses are equal to within the accuracy of the experiment." Otherwise you cannot. In short, you have to do some error analysis.
 
The thing is, I am doing all of this numerically - but one system is larger than the other (i.e. more data points), so the result I get should - in principle - have converged more. The good news is that I get the same answer, which means that my original measurements (the "small" system) are correct.
 
I am not sure what you mean by "numerically". Where did you get the numbers? Were they just given to you, or were they the results of numerically processed data from an experiment that you conducted? If you have performed an experiment, then you should have a feeling of its percent accuracy.
 
They are numbers that I was given - I think they just describe realistic systems, not necessarily real systems.
 
Then all you can say is that "the masses are equal to within x percent".
 
Just to be 100% clear: So if I get e.g. m = 0.10 kg and m=0.11 kg, then they are the same to within 10%?
 
Correct.
 

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