Meters to the -3rd Power: 5.1*10^-5m

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Discussion Overview

The discussion revolves around the interpretation and calculation of units involving meters raised to negative powers, specifically focusing on the multiplication of meters and meters to the negative third power. Participants explore the implications of these units in terms of density and dimensional analysis.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks about the unit resulting from multiplying meters by meters to the negative third power, seeking clarification on the appropriate unit for the answer.
  • Another participant explains that "per meter cubed" corresponds to the unit m^-3, indicating that this is a common dimension for number density.
  • A participant expresses uncertainty about the unit to use when multiplying specific values, questioning whether "per meter cubed" refers to m^-3 or to the product of m and m^-3.
  • A later reply clarifies that "per meter cubed" is indeed 1/m^3, while the product of m and m^-3 results in m^-2 or 1/m^2.

Areas of Agreement / Disagreement

Participants express differing interpretations regarding the units involved in the calculations, indicating that multiple competing views remain on the correct understanding of the dimensional analysis.

Contextual Notes

Some participants may be operating under different assumptions about the context of the units, and there is an unresolved aspect regarding the application of these units in specific calculations.

you_of_eh
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What would meters*meters^-3 be?

Ex: 5.1*10^-5m(1.314*10^18m^-4)

[m=meters]
 
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It would be read as "per meter cubed." Number density has this dimension, e.g. "100 molecules per meter cubed."

- Warren
 
OK but..

I have to do a calculation multiplying m and m^-3 and I don't know what unit to use for the answer.

Say..5m*5m^-3= 25..what unit?

Also, when you say "per meter cubed", are you talking about m^-3? or m*m^-3?

Thanks for your response.
 
per meter cubed is 1/m^3, but m*m^-3 is m^-2 or 1/m^2
 

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