Multiplying 1-digit numbers by 10, 100, and 1000 | Math | 4th grade | Khan Academy

Let's talk about multiplying by 10, 100, and 1,000. There's some cool number patterns that happen with each of these, so let's start here with something like 4 * 10—one that maybe we're comfortable with or already know.

4 * 10 would be the same as saying four tens, four tens, and four tens. One way we could represent that is a 10 plus a second 10, it's a third 10 plus a fourth 10, or four tens. And now let's count that: 10 + 10 is 20; + 10 is 30; + 10 is 40. So our solution is 40, or a four with a zero.

This is the pattern that we've seen before. When we multiply 4 * 10, we keep our whole number of four, and we add a zero to the end.

For another example of that, let’s consider something like 8 * 10. Well, 8 * 10 is the same as 8 tens. This time, let's just count them. If we count 8 tens, it'll be 10, 20, 30, 40, 50, 60, 70, 80.

So, when I counted 8 tens, the solution was 80, or an 8 with a zero on the end. So, when we multiply a whole number by 10, the pattern is that we end up adding a zero to the end of our whole number.

Now, let’s take what we already know about tens and apply it to hundreds. Something like, let’s say, 2 * 100. There are a couple of ways we can think about this. One way is to say that this is the same as two hundreds.

Hundreds, which is 100 plus another 100. There is quite literally two hundreds, which is a total of two 100, or two with two zeros on the end. Now we have two zeros on the end.

Another way to think about this is 2 * 100. Instead of saying times 100, we could say times 10 times 10 because 10 * 10 is the same as 100. We know that 2 * 10 is a two with a zero on the end, which is 20, and 20 * 10 then will be 20 with a zero on the end.

Because we multiplied by 10 twice, we added two zeros. Multiplying by 100 is just that—it’s exactly that. It's multiplying by 10 twice. So, if times 10 adds one zero, then times 100, or times 10 twice, adds two zeros to our answer.

We can go even further and think about thousands. Let's try something like 9 * 1,000. Well, we could think of this as 9,000. If we have 9 thousands, then we have 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000.

So when I counted 1,000 times, our solution was 9,000, or looking at the numbers—a nine, our original whole number, with three zeros after it. So, 9 * 1,000 is 9,000, or 9 with three zeros.

We can go back to what we did before, thinking about this in terms of tens. We've worked out why multiplying by 10 adds a zero, so let’s think about 1,000 in terms of 10. 1,000 is equal to 10 * 10 * 10.

10 * 10 is 100, and 100 is 1,000. So instead of 1,000, we can write 10 * 10 * 10. These are equivalent, and so when we multiply a number by 10, we add a zero, but here we're multiplying by three tens, so we add three zeros.

Let’s look at that all as one pattern. Let’s say, for example, the number 7, and let’s multiply it by 10, by 100, and by 1,000, and see what happens.

7 * 10 is going to be 7 with 1 zero. So we have 70. 7 * 100 will be 7 with two zeros because again, 100 is the same as 10 * 10. So this is 7 * 10 twice, so we have two zeros.

7 * 1,000 will be 7,000, or 7 with three zeros, because 1,000 is equal to 10 * 10 * 10, or three tens, so we add 1, 2, 3 zeros.

So, we can see the pattern here: when we multiply by 10, which has one zero, we add one zero to the end of our whole number. When we multiply a whole number by 100, which has two zeros, we add two zeros for hundreds. And for thousands, when we multiply by 1,000, we’ll add three zeros to the end of a whole number.