Each step down is ×1000. M → mM → µM → nM.
So 1 mM = 1000 µM = 1,000,000 nM.
Molar and mass units are linked by molecular weight:
mg/mL = mM × MW ÷ 1000
mM = mg/mL ÷ MW × 1000
Why you need MW: molarity counts molecules, mass counts weight.
A big molecule weighs more per molecule, so the same mM is a higher mg/mL.
1% (w/v) = 1 g per 100 mL = 10 mg/mL.
1X from a 10X stock = dilute 1:10.