Multiplying with 10, 100 and 1000

Look at this building. Two rows with … ten windows in each row. In total there are … 20 windows. 2 times 10 is 20. This building has three rows with 10 windows, that is … 30 windows altogether.

3 times 10 is 30. And when we add another storey, making it four rows with ten windows, we end up with … 40 windows on the wall. 4 times 10 is 40. There is a pattern here. Can you see it?

When we multiply a whole number by 10 we get a product which resembles the whole number, but with an extra zero at the end! 5 times 10? Yes, add a zero to the five. The product is 50. 9 times 10?

90. 282 times 10? Same thing here. Add a zero, and there is the answer. 2820.

Let’s stay with the number 282 for a while. It has three digits: a two, an eight, and another two. Now, let’s consider the place values of each of these digits. The first two is in the hundreds position, so it means 200. Then there’s the eight in the tens position, so that means eighty.

And the second two, that’s in the ones position, so that just means two. And now let’s carry out the multiplication again: 282 times 10 equals 2820. If we write the calculation like this, it’s easier to see what happens We have shifted all the digits one place to the left. So each digit now has a different place value! The first two no longer means two hundred, but two thousand.

The eight now means eight hundred, and the second two means twenty. And the new digit in the ones position is zero! So, when we say that we “add a zero at the end”, what we are really doing is shifting all the digits one step to the left, so that their place value increases ten times. Let’s do some more calculations! We’ll calculate whole numbers times 100.

The number 100 has two zeros at the end, so we will write two zeros to get the product. 2 times 100? Write two zeros after the two. 200. 5 times 100?

Write two zeros. 500. 8 times 100 equals 800. And 863 times 100 equals 863 with two zeros at the end. 86 300.

If we multiply with 1000 we need to add three zeros. 12 times 1000? Write the number 12, and add three zeros. This is 12 000. And the digits 1 and 2 have new place values.

The two now means two thousand, and the one means ten thousand. The pattern we have just seen also applies when we multiply with even larger numbers. A whole number times 1 000 000? Add six zeros to the whole number. And if we need to calculate 17 times one billion, how many zeros do we need to add to 17 to get the product?

Yes, write nine zeros. This is 17 000 000 000.