can anybody tell me why in the U.S are change gose by 1,5,10,25 but the cash part gose 1,5,10,20. why is this why not 1,5,10,20-1,5,10,20
or 1,5,10,25-1,5,10,25.

Well, without 1's or pennies, we can give any number of 5-cent-intervals using only 4 coins:

5
10
10-5
10-10
25
25-5
25-10
25-10-5
25-10-10
50
50-5
50-10
50-10-5
50-10-10
50-25
50-25-5
50-25-10
50-25-10-5
50-25-10-10
With bills, we use 1-(2)-5-10-20-50-100 because by near-doubling, we spend maximum money with minimum bills.

At least part of it is based on the historical popularity of certain coins. During the 19th century, the US had a larger variety of coins in circulation. There were gold coins ranging from $1 to $20 in value, there were 2 cent pieces, 3 cent pieces, and 20 cent pieces. In the early half of the 19th century, what we would call a penny, namely a one cent piece, was actually a coin larger than today's quarter while what we would call a nickel was actually a tiny coin (smaller than today's dime) worth 5 cents called a "half-dime". Some denominations were rarely used due to the fact that they were so close to another that was already firmly entrenched in everyday life. The 20 cent piece only lived a few years because no one felt it was necessary to have a 20 cent piece AND a quarter. The $4 gold piece called the Stella was virtually unused because there was already a $5 piece in place. Even today, $1 coins are pretty much unused in the population because $1 bills are so familiar to us (and because it's much easier to carry several dollar bills than it is dollar coins). There are actually quite a few $1 coins in circulation today-it's just that many people see them for the first time and stow them away because they have the mindset that they are rare and collectible just because they're new. That's why you don't see many around.

I know this didn't exactly answer your question, but I hope it provided some insight

Printing fewer big denominations of bills does cut down on having to keep much more track on counterfeiting and may cut down on the speed of inflation.

Thank you everybody.

However, tsaeb, wallets get very fat and bulksy if there are too many 1s floating around. There is a statistic online somewhere regarding how much of each is printed a year, but I can't remember the link.