How Many Significant Figures Does Physics Agree On?

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    Significant figures
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Discussion Overview

The discussion revolves around the conventions and agreements among physicists regarding the use of significant figures in calculations. It explores how significant figures are determined based on the precision of the values used in calculations, with examples provided to illustrate different scenarios.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant asserts that the number of significant figures in a result should match the least precise value used in the calculation, using Ohm's law as an example.
  • Another participant counters that if the current and resistance values are given with different precisions, the calculated voltage should reflect that precision more accurately.
  • Some participants question the relevance of trailing zeros after a decimal point, suggesting that they may not always be significant depending on the measuring instrument's precision.
  • A participant argues that zeros to the right of a decimal point can be significant, particularly when measurements are taken with precise instruments.
  • There is a discussion about the treatment of zeros in integers versus decimal numbers, highlighting that additional context is necessary to determine the significance of zeros in certain cases.

Areas of Agreement / Disagreement

Participants express differing views on the significance of zeros and the rules governing significant figures, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Some assumptions about the precision of measuring instruments and the context in which numbers are presented may not be fully addressed, leading to potential ambiguity in the discussion.

fs93
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What do physicists agree on the number of significant figures to use?

I've done some research and I found that the answer has the same number of significant figures as the least precise value used to calculate it.

ex: V=IR

[I=1.25474]
[R=5.2]

Hence, voltage is simply 6.5?

Thanks,

FS
 
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But if [I=1.25474],[R=5.20000], the voltage is 6.52468 V.
 
Is that so? Aren't zeros after a decimal completely irrelevant? Especially considering that an ammeter will give you a reading of one decimal place.
 
fs93 said:
Is that so? Aren't zeros after a decimal completely irrelevant? Especially considering that an ammeter will give you a reading of one decimal place.

They are relevant if they are the amper-meter readings. In case of one decimal place they are irrelevant, one does not write them, and your post calculation is correct.
 
Gotcha. Thanks Bob for Short :)
 
If I understand correctly (and it's been 2 decades or more), the zeros to the right can indeed count.

If I weigh a sample on a microgram scale and it comes out as 100.00g, surely that is accurate to five sig digs.
 
Yes, the general practice is to assume that "unnecessary" zeroes at the end are significant, and that if they were not significant, the writer would have omitted them.

This doesn't apply if the number is given as an integer without a decimal point. In that case, all the zeroes at the end are necessary, but not necessarily significant in terms of precision. If you're given the number 230000 without any additional information, it's impossible to say whether it has 2, 3, 4, 5, or 6 significant figures. However, if you're given 230000.0, then you can generally assume that it has 7 significant figures.
 

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