Interpreting Units: km-1 Explained

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The term "km-1" is definitively interpreted as 1/km, which translates to 1/(103 m), equating to 10-3 m-1. This notation signifies "per kilometre" or "per thousand metres." The discussion highlights a common misconception regarding the scaling of units in the International System of Units (SI), emphasizing that the scaling prefix is more closely associated with the unit than the superscript, contrary to typical algebraic expectations.

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Danny-Boy
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Apologies for the newbie question, but when it is written km-1 does that mean (103m)-1 or 103(m-1)?

Thanks in advance!
 
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Just follow the rules:

km-1 means 1/km which means 1/(103 m) which means 10-3 m-1
 
"km to the minus one" means "per kilometre" or "per thousand metres"!
 
The former. The scaling prefix sticks tighter than the superscript, unlike what you expect from Algebra. This is one of the criticisms of SI, in that units of higher dimension scale too extreme.
 

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