In Lehninger's Principle of Biochemistry Pg. $14$, this is the definition for molecular weight (relative molecular mass):

The molecular weight of a substance is defined as the ratio of the mass of a molecule of that substance to one-twelfth the mass of carbon- $12$ ($12$C). Since $M_r$ is a ratio, it is dimensionless—it has no associated units.

What I do not understand is how we find the mass of the molecule in the beginning. What unit would we use?

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    $\begingroup$ For a great explanation (and a great read) see To land on a Dalton by Susan Dewhurst and (if you are 'into' Mathematica) see here. As SD points out, 'molecular weight' is frowned on (use relative molecular masss (dimensionsless) or molecular mass (units of Da or amu)) $\endgroup$ – user1136 Oct 16 at 18:35
  • $\begingroup$ @user1136 The phrase "molecular weight" may be frowned on, but I doubt it's ever going to go away unless all the reagent makers get on board. I don't think I've ever seen a protein standard marketed as a "molecular mass marker"... $\endgroup$ – MattDMo Oct 16 at 18:44
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    $\begingroup$ @user1136 I agree with you that the most precise term should be used, I just wanted to make the point that there is a lot of historical weight (so to speak) on the term "molecular weight", and I don't think its usage will decrease until reagent makers get on board. $\endgroup$ – MattDMo Oct 16 at 18:57
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    $\begingroup$ I voted to close this question as off-topic as it is a general chemistry question. $\endgroup$ – David Nov 5 at 12:04

The mass of a biological molecule is evaluated by the process of Mass Spectrometry (specifically MS/MS or MALDI-TOF). These are an improved version of Mass Spectrometry(MS) and results from the works of physical chemists.In a nutshell, you can ionize the molecule. It dissociates into several ionized particles. Then subject them to a magnetic field and an electrical field at the same time. The ionized particles take a curved route while moving , and the amount of curve depends on m/q of molecule ( mass of particle (in kg) and charge of it)

see https://en.wikipedia.org/wiki/Mass_spectrometry

Molecular weight is dimensionless indeed. However one may add Dalton/amu/u "False" physical units for better understanding. The best other example in physics is radians. Angles are defined in radians in physics. But they are dimensionless.

In Circular motion , we have these formula :

v = w * r

teta = w * t

see: this

unit of v is (meter per second) and unit of r is (meter). therefore the unit of w (omega) is s^(-1) . unit of w is " s^(-1) " while the unit of t is "s".

So teta is dimensionless although we describe it as radians for better understanding

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