Why do you place a zero in the ones place of the second partial product in a multiplication problem?

Answer 1

Consider the example 234 x 26.

When multiplying out, you do the ones digit first, then the tens digit:

• ones: 234 x 6 = 1404
• tens: 234 x 2 = 468

and then add the results together.

However, the value of the tens digit is the_digit x 10. So in this example, the tens digit is not worth two (2) but twenty (20 = 2 x 10). Thus the correct value of multiplying by the tens digit is:

• 234 x 2 x 10 = 468 x 10 = 4680

(The correct sum is: 234 x 26 = 1406 + 4680 = 6084)

So when multiplying by the tens digit there will be a zero (0) on the end.

Similarly when multiplying by a hundreds digit there will be two zeros (00) on the end.

To avoid forgetting to do this, the zero(s) is(are) normally written in first before doing the multiplication by the tens (hundreds, etc) digit.