Why is (European) money in units of $1,2,5,10,20,50, \cdots\;$?

Question

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 :

• Postage stamp problem (Wikipedia)
• Coin problem (Wikipedia)
• Change-making problem (Wikipedia)
• Preferred number (Wikipedia)

Maybe those references form already an answer to the question.

Answer 1

As already stated by Darth Geek, $1$, $2$, and $5$ are the proper divisors of $10$. This means that all sufficiently large powers of $10$ are achievable by using a finite number of any chosen coin/note. Mental math is also really easy (one $10$, two $5$'s, five $2$'s, etc...).

Additionally, these numbers form an approximate geometric sequence. If you are a retail store manager and want to (approximately) double the price of every good, simply choose the next largest coin/note size. For example, a $5$ coin item would now cost $10$ coins, while a $10$ coin item would be $20$.

Here are some related resources:

• Preferred Numbers
• 1-2-5 Series
• E Series

Answer 2

I think it's a mix between two facts:

1.- If Alice wants to buy something from Bob and both Alice and Bob have each one of every coin and note, it is guaranteed that Alice can buy that something regardless of the price (all numbers can be constructed with the money from Alice and the change that Bob can give her). The simplest way to do this would be to use powers of three for the currency. This is where the second fact comes in.

2.- We use the decimal system and 1,2,5 are the divisors of 10. So it makes it easier to compute what selections of coins and notes to use to pay for goods and serices.