Video: Multiplying by 10, 100, and 1000

In this video, we will learn how to multiply a one- or two-digit number by 10, 100, and 1000.

14:49

Video Transcript

Multiplying by 10, 100, and 1,000

In this video, we’re going to learn how to multiply a one- or a two-digit number by 10, 100, or 1,000. Let’s begin with a quick reminder. This is to do with place value. And it’s something we should know already. And that’s that each column to the left of another one has a value 10 times greater. So here’s a single one. But 10 of these ones are worth one of the next column along, one 10. And if we have 10 10s, that’s the same as one of the next column along, one 100. 10 100s are the same as 1,000. And if we have 10 of these, it’s the same as one lot of 10,000, which we don’t have a place value block for because it would be too large. So we’ll write the digit one in the ten thousands place.

So as we move from right to left across this place value grid, we multiply by 10 each time to get to the next column. Now I’m sure you knew this already, but we’re going to see as this video continues how useful it’s going to be when it comes to multiplying numbers by 10, 100, and 1,000.

Let’s begin with a really simple calculation. What is five times one? The answer, of course, is the same as five ones. Five times one equals five. Now we can build on this really simple number fact. And hopefully you’ll be able to see how we can use it to help us. Let’s now multiply by 10. What is five times 10? This time, the answer is going to be the same as five lots of one 10 or five 10s. Five times 10 is 50. Do you notice anything about our two answers? We’ll come back to this in a moment. In the meantime, let’s multiply five by 100.

I’m sure you’re getting the hang of this. This is going to be worth five 100s or 500 and one more. Five multiplied by 1,000, well, I’m sure you can predict how to model this. Five lots of 1,000, of course, are worth 5,000. So we’ve multiplied the same number here by one, 10, 100, and 1,000. Now what do you notice about our answers? Did you spot? Each one contains the number that we started with, five. And this brings us on to a useful fact to remember. If we’re multiplying by 10, 100, or 1,000, the digits in the number that we’re multiplying by 10, 100, or 1,000 — in this case, it’s the number five — they don’t change.

So if we multiplied nine by 10, 100, or 1,000, our answers would all have the digit nine in them. If we multiply the number 28 by 10, 100, or 1,000, all our answers would have the digits two and eight in them. And even though we’re not gonna be dealing with such large numbers in this video, the answer to the question the blue monster is asking is yes. If we multiplied 7,654 by 100, the answer is going to contain the digits seven, six, five, and four. And that’s because when we multiply any number by 10, 100, or 1,000, something happens to those digits. Let’s look a little more closely at what goes on.

Let’s imagine that we want to find the answer to 26 multiplied by 10. The digit two in the number 26 has a value of two 10s. It’s in the tens place. So we could put a digit card in the tens place, or we could use two 10s counters to model the number. Then the six digit in 26 is worth six ones. So again we could put a digit card in the ones place or we could use six ones counters. Both of these models show the number 26. So now we need to multiply it by 10.

Now remember, as we’ve pointed out already, we know that the answer is going to contain a two and a six in it. But what’s going to happen to these digits? Firstly, let’s think about the digit two. At the moment, it’s in the tens place. It has a value of two 10s. But if we multiply this digit by 10, it’s not going to be worth two 10s anymore. It’s going to be worth 10 times as much. And this brings us back to what we learned right at the start of the video. Each column or place to the left of another one is worth 10 times as much. So if we multiply them by 10, our two 10s counters are going to be worth two 100s instead, and our digit two is going to shift one place to the left. It’s now worth two 100s.

And a similar thing is going to happen to our six digit. At the moment, it’s worth six ones. But as soon as we multiply these six ones by 10, they’re going to be worth 10 times as large, six 10s now. And so the digit six needs to move from where it is now into a column that’s worth 10 times as much. It’s going to shift into the tens place. And to show that these two digits have now shifted one place to the left, we need to show the empty ones column. And that’s why we write a zero as a placeholder. 26 times 10 equals 260.

When we multiply a number by 10, each digit now has a value 10 times greater. This means that the digits shift one place to the left. Let’s try solving a problem now that’s all about multiplying a number by 10.

Complete: 10 multiplied by what equals 120.

In this question, we’re multiplying a number by 10 to get the answer 120. But what is our missing number? Often, when we’re finding a missing fact in a multiplication like this, we could use division to help, the inverse operation. In other words, we could divide 120 by 10 to find the answer. But there’s another way to find our missing number. And that’s to use what we know about what happens to numbers when they’re multiplied by 10.

We know that when a number is multiplied by 10, each of its digits becomes worth 10 times as large as it did before. So just as an example, if we multiply eight by 10, the digit eight is no longer worth eight ones. It’s now worth 10 times as much, eight 10s. We started off with a digit eight, and our answer also contains a digit eight. It’s just shifted one place to the left. Now, if we look at our calculation, we know that this is exactly what’s happened to the number we’ve multiplied by 10. Its digits must have shifted one place to the left. And the answer is 120. This is the number we’ve ended up with.

The digit two in our answer has a value of two 10s or 20. But this is after it’s been multiplied by 10. What was it worth before it was multiplied by 10? Instead of two 10s, it must have had a value of two ones. The digit one in our answer has a value of 100. But this is 10 times greater than what it was to begin with. So in our starting number, the one must have had a value of one 10. It looks like the number that we’ve multiplied by 10 is 12. And as we’ve multiplied it by 10, each digit’s value has become 10 times as large and has shifted one place to the left.

We’ve used our knowledge of how digits change when we multiply a number by 10 to help find the missing factor. 10 times 12 equals 120. Our missing number is 12.

Now that we understand what happens to a number when we multiply it by 10, we can use this to help us understand what happens to the numbers when we multiply them by 100 or 1,000. We know that 100 is the same as 10 times 10. So multiplying a number by 100 is the same as multiplying it by 10 and then 10 again. And we know 1,000 is the same as 10 times 100. And as we’ve just said, 100 is the same as 10 times 10. So if we multiply a number by 10 three times, this is the same as multiplying by 1,000.

Now, how does this help us? It’s time to come back to our place value grid again. We know that shifting a digit from one column to the next one on the left is the same as multiplying it by 10 or making it 10 times greater. So if we want to multiply a number by 100, which we’ve said is the same as multiplying by 10 and then 10 again, this is the same as two jumps to the left. So if we want to find the answer to 13 times 100, for example, the digit one, which was worth one 10, is going to shift once, twice and is now worth 1,000. And the digit three, which is worth three ones to begin with, is going to shift one, two places to the left and is now worth three 100s. And we’re going to need two zeros to show our two empty columns.

We started with the number 13, and look how our answer contains the digits one and three. 13 multiplied by 100 equals 1,300. And I’m sure you can work out what happens if we want to multiply a number by 1,000. If we want to find the answer to 27 times 1,000, we’re going to need to multiply each digit by 10 and then 10 again and then 10 again. Our two digit is now going to be worth two lots of 10,000 or 20,000. And if we shift the seven digit three places to the left, it’s now going to be worth seven 1,000s. 27 multiplied by 1,000 equals 27,000.

So you can see that the methods we use to multiply a number by 10, 100, or 1,000 are all linked. Let’s answer some questions where we have to multiply some numbers by 100 or 1,000 now.

Calculate 100 multiplied by 96.

From our knowledge of multiplication, we know that we can multiply two numbers in different orders and they’ll still give the same answer. So we could think of this multiplication as 96 times 100. To solve this problem, we can use what we know of place value to help us because special things happen to the digits in a number when they’re multiplied by 100. Let’s use place value counters to help us here.

The number 96 is made up of nine 10s and six ones. Let’s think about what happens to our nine 10s to begin with if we multiply these by 100. We know if we multiplied these nine 10s by 10, they’d become worth nine 100s and the digit nine would shift one place to the left. But we don’t want to multiply our nine 10s just by 10; we want to multiply them by 100. We need to multiply them by 10 again. They’re going to be worth nine 1,000s. And this is the same as shifting the digit nine two places to the left.

Now we need to do the same with our six ones. Multiplying them by 100 means shifting them once, twice. Our six ones are now worth six 100s. If we multiply any number by 100, each of its digits becomes worth 100 times greater. And so they shift two places to the left. That’s how we know 100 multiplied by 96 equals 9,600.

Calculate 12 multiplied by 1,000.

The number 12 is made up of one 10 and two ones. But as soon as we multiply this number by 1,000, each of these digits is going to be worth 1,000 times as much as it does at the moment. We know that when we’re thinking about the place value in a number, as we move from right to left, each place to the left of another one is worth 10 times as much. So we know if we want to multiply a number by 10, we shift the digits one place to the left. To multiply by 100 is the same as shifting the digits two places to the left. And to multiply by 1,000 is the same as shifting the digits three places to the left.

We need to multiply the number 12 by 1,000, so we can write it in our place value grid and then move our digits once, twice, three times to the left. And to show that they’ve moved, we better write in some zeros to mark the three empty columns. We know that multiplying a number by 1,000 is the same as multiplying it by 10, by 10 again, and then by 10 again. We also know that each time we multiply by 10, we just need to shift the digits of a number one place to the left. So to multiply by 1,000, that’s just a shift of three places to the left. 12 multiplied by 1,000 equals 12,000.

So what have we learned in this video? We’ve learned how to multiply one- or two-digit numbers by 10, 100, and 1,000. We’ve learned to do this by thinking about the value of each digit and also how digits shift when we multiply by 10, by 100, or by 1,000.

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