These calculations are best set out on a piece of paper (i.e. without a calculator). Do not try to use a formula — use the definition of molarity followed by logic involving simple proportion.
Example Question:
How many μmol in 50 μl of 100 mM KCl?
Strategy:
Express mM as its definition — mmol per litre
Convert to μmol per litre because answer requires μmol
Convert to μmol per μlitre because volume is in μlitre
Convert to μmol per 50 μlitre (the volume in this case)
Worked Answer:
100 mM = 100 mmol/litre
100 mM = 100 x 103μmol/litre
100 mM = 100 x 103 x 10–6 μmol/μlitre
100 mM = 50 x 100 x 103 x 10–6 μmol/50 μlitre
i.e. 5 μmol in 50 μlitre of 100 mM KCl
The three-stage version of these calculations illustrates this approach.