In the old days, in the Netherlands, we had 1 ct (cent), 5 ct (stuiver),
10 ct (dubbeltje), 25 ct (kwartje), 1 gld (gulden), 2.5 gld (rijksdaalder),
10 gld (tientje), ...
And then they decided we should pay in Euros for the
rest of our lives.
A picture says more than a thousand words:
Yes, everybody knows that it's practical. But why this particular choice?
What's wrong with the old coins sequence? What's good with the $1,2,5,10,20,50, \cdots\;$ sequence?
EDIT. Gathered some evidence that the question as stated is indeed mathematical :
Maybe those references form already an answer to the question.