Currency denominations (coins and bills) are usually based on numbers like 1, 2, 5, 10, 25, 50, 100, 200, etc. An extreme example is that Japanese yen are deno

Currency denominations (coins and bills) are usually based on numbers like 1, 2, 5, 10, 25, 50, 100, 200, etc. An extreme example is that Japanese yen are denominated as 1, 5, 10, 50, 100, 500, 1000, 2000(uncommon), 5000, 10000. But I noticed that it takes a lot of 1's to pay or make change, whereas the 5's are less used. What if we use denominations like 1 and 3 instead? The benefit is that the ratio 1:3 is similar to the ratio 3:10, so they are more evenly spaced on a logarithmic scale. Specifically, I'd like to explore what happens if the denominations are 1, 3, 10, 30, 100, 300, 1000, 3000, etc...