Interpreting Units: km-1 Explained

[Danny-Boy]

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

Thanks in advance!

 

[cepheid]

Just follow the rules:

km^-1 means 1/km which means 1/(10³ m) which means 10^-3 m^-1

 

[sophiecentaur]

"km to the minus one" means "per kilometre" or "per thousand metres"!

 

[JDługosz]

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.