Thanks for your question. A mole is an Avagadro's number of
particles. Avagadro's number is 6.02x10^23. The significance of this
number is that for this number of particles of any homogeneous
substance (atoms, molecules), the weight in grams will equal the
substance's atomic weight in Daltons. An example: If you have
6.02x10^23 hydrogen atoms, each of which has a mass of 1 Dalton, then
the mass of this large number of hydrogen atoms is 1 gram.
Now to your question. 100 fmoles is 100 femtomoles of insulin
receptors. You don't need to know the mass of the insulin receptors
to solve the problem.
100 femtomoles = 100 x (10^-15) moles [femto means 10^-15]
So, we have 100 x 10^-15 moles of insulin receptors on 10^6 beta cells.
If we assume that the receptors are distributed evenly (a big
assumption in vivo), then we have
100 x 10^-15 x 6.02 x 10^23 receptors / 10^6 beta cells = 6.02 x 10^4
receptors / cell = 60,200 receptors / cell.
Final answer: 60,200 receptors / cell
Here's a page on moles and Avogadro's number for more details:
If you're interested, here is a page on Avogadro himself:
I hope this information was helpful. Feel free to ask for clarification.