I did this in high school when we weren't allowed a calculator during tests and got into an argument with a teacher who told me that it is impossible to do this in your head so I must have cheated. A short demonstration on random numbers sufficed. I've taught my kids the method and they are now set up for similar arguments ;)
The hardest part if you want to generate more digits is to keep track of the intermediary sum during the multiplication, that's why I never got past three significant digits. That would be an interesting little contest though!
The hardest part if you want to generate more digits is to keep track of the intermediary sum during the multiplication, that's why I never got past three significant digits. That would be an interesting little contest though!