How do I convert ( glucose concentration ) µg per ml into µM? For example 10 µg per ml?

The molar mass of glucose (see: wiki, or calculate yourself) is 180.16 g/mol

 

You have the amount in g/l (µg per ml to g/l should be easy).

 

You know how many g/mol glucose is.

 

So, this enables you to calculate how many mol/l (M = mol/l). Then to go to µM is easy again.

 

The important bits here are the units (g/l, g/mol and mol/l)

 

[math] g/l * mol/g = mol/l [/math]

However, the molar mass is not in mol/g, but in g/mol. Don't panic. In stead of multiplying, you need to divide by the molar mass.

 

[math] 1 / (g/mol) = mol/g [/math]!

 

So, the first thing you must to is convert all your numbers to the right units (only containing "g", "l" and "mol", and no "µg", "ml" or "µM", then do the calclation, and then convert the result to the unit you want (go from M to µM).