Multiplying large numbers: counting zeroes

This can contains 30 sardines. This cardboard box contains 20 of these cans. How many sardines are there in total in the cardboard box? 20 cans, 30 sardines in each. Altogether there are 20 times 30 sardines.

20 times 30. These numbers are not in the times table, so we’ll use a trick. Like this: We’ll start by moving the zeros to the side. We’re left with 2 times 3, and this is no problem. 2 times 3 is 6.

Let’s put the zeros back and place them behind the six. And there is the product: 20 times 30 equals 600. Let’s try again, with slightly larger numbers. 40 times 80. You can try yourself first.

Pause the film and calculate the product. Remove the zeros, and keep them in mind. It’s important to recall how many zeros there are. We’re left with 4 times 8, and this is 32. Then we add the two zeros we removed.

The answer to 40 times 80 is 3200. So this is the trick: Remove all the zeros. Calculate the multiplication without the zeros. Place the zeros behind the product. But remember: it only works with zeros written last in the factors.

It won’t work if the zeros are in the middle, like in the number 408. Does the trick work to calculate 50 times 80? Oh yes, the zeros are last, so we’re good. We take two zeros aside. 5 times 8 is 40.

Bring back the two zeros, and the product is 4000. Does the trick work here? 202 times 8. No! The zero is not last in the factor, and so it doesn’t work.

We cannot remove a zero from the middle of a number. But, again, if the zeros are last in a factor, it always works. It doesn’t matter how large the numbers are and how many zeros there are. 9000 times 40? Pause the film and try for yourself.

Take the zeros to the side, and keep the number of zeros in mind. 4 of them. 9 times 4 is 36, and then we add the zeros. 9000 times 40 is 360 000. One last task.

500 times 5000. Try for yourself. There are five zeros to keep in mind. Then we calculate 5 times 5, and this is 25. Bring back the zeros, and the product is 2 500 000.

Back to the sardines. So we have 30 sardines in each can, 20 cans in each box, and 80 boxes in this lorry. How many sardines are there altogether in the lorry? 30 times 20 times 80. Hmm, here there are three factors to multiply, but we do the calculation in just the same way.

Move the zeros to the side, and remember how many there are. Three. Then: calculate 3 times 2, this is 6… times 8, this is 48. And then bring the zeros back and write them after 48. So we have in total 48 000 sardines in this delivery.