This is somewhat misleading. Yes, it's true if 3 * 123456789 counts as one multiplication. But if you're doing the 'old' version you implement it as 9 si

This is somewhat misleading. Yes, it's true if 3 * 123456789 counts as one multiplication. But if you're doing the 'old' version you implement it as 9 single digit multiplications: 3*9, 3*8,....,3*1 all written down with appropriate carrying. If you do it with the new method you again get 9 'single' digit multiplications: 3*9, 3*80, ..., 3*100000000 which you then add up. --- The old methods efficiency comes from writing the steps out in a compact notation, not from reducing the number of multiplications or additions.