Why are notes better than coins?

Notes are not necessarily better. There are reasons for each form of money.

Notes (bills) are useful for large denominations because they can be easily printed in various amounts, colors, and sizes to make them distinctive. Large denomination bills don't get a lot of use so they stay in circulation for a long time and are relatively economical to make, even given the need for strong anti-counterfeiting measures. They also are easier to carry than the number of coins needed to represent an equivalent value.

Coins are better for small denominations because they receive a lot of use in making change. Bills wear out very quickly when used heavily, while coins stay in circulation for 30 to 50 years. Bills have a relatively high fixed cost to print, so they would be much more expensive if they had to be replaced frequently. In addition the fixed cost could actually be higher than the amount represented.

Coins are also much more efficient for use in vending machines because they can be handled by electro-mechanical acceptors that are straightforward and simple to repair, versus computerized bill-readers that need special software and cost up to $500 apiece.

Many other countries have replaced their low-denomination notes with coins for these reasons. The U.S. is one of the few countries that still issues bills for $1 amounts. Nearly half of all bills printed are ones, and it costs the government almost a billion dollars a year more to print them than it would cost to replace them all with coins and use $2 bills instead. However, a combination of strong traditions and powerful lobbying by the company than makes the paper for $1 bills has prevented the U.S. from eliminating its $1 bill.