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.

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The old methods efficiency comes from writing the steps out in a compact notation, not from reducing the number of multiplications or additions.