How are One-Dimensional Numbers Useful (Coupling Constants)

[TheDemx27]

How would it make any sense to use dimensionless numbers to represent physical things?

From wikipedia:

The coupling constant arises naturally in a quantum field theory. A special role is played in relativistic quantum theories by coupling constants which are dimensionless, i.e., are pure numbers.

If you are comparing the strength of forces, and you are using these numbers to do so, I would have thought that these numbers would represent units of - well, force.

Clearly I must be missing something.

Thanks.

 

[Meir Achuz]

The size of any constant with units is ambiguous. Is g=980 cm/sec^2 large or 0.0098 km/sec^2 small?
Expressed as a dimensionless number in 'natural' units, the electric charge of the electron is e^2=1/137 regardless of what units were used before it was made dimensionless, so the EM interaction is seen to be small.