All the other denominations in bills are paralleled in coins - 1, 5, 20, 50, 100 (the 1 dollar coin). But instead of having a 20-cent coin we use a quarter (or instead of having a $25 bill we have a $20). Is there some historical rhyme or reason behind this asymmetry? How were the denominations of coins to be minted and bills to be printed chosen in the first place?
The dollar is the base unit of our currency, not $100. Our coin currency represents fractions of that dollar and 1/4 is a far more useful and logical fraction than 1/5.
Going into larger bills having more "rounded" numbers is more logical.