What is the relationship between one hundredth and one thousandth?

If one bead on a bead string represents one thousandth, how many beads would you need to represent one?

When you are comparing the decimal numbers 1.234 and 1.256, which place value column is the most important to decide which is the largest?

If I am representing the decimal number 3.609 using place value counters, which place value column will be empty?

Place Value to 3 Decimal Places Quiz

﻿Hi again everyone, and welcome back. Today's lesson is going to be on multiplying and dividing by 10, a 100 and a 1000. And we're going to include some decimal numbers as well, because we were working on them. Before we start the lesson, I'm just going to give you a little bit of a joke. So what do you call a boomerang that doesn't come back? Not sure? A stick. Okay on that note, I think it's time to start the lesson. Now, bit of a review of the lesson, just to give us an idea of what we're going to be up to. We're going to need to multiply it by 10, a 100, and a 1000, we're then going to divide by 10, a 100 and a 1000, making sure that we're really clear about what's happening, then we're going to practise it in our independent task. Okay, moving on then make sure that you've got as always that pencil and paper ready to make some jottings, ready to make some notes and to engage in the learning as much as possible. Straight onto multiplying by 10, a 100 and a 1000 then. Now really, really important to use during this, during this lesson is a place value chart. It's going to really support us to prove and help our understanding. So if you want to, if you have a whiteboard or just a piece of paper, you might want to create this place value chart in order to be able to help you during this lesson, okay? So you might want to pause the video now to create one if you've got a whiteboard that you could do on, even better. When you've done that, let's get started then. So let's have a look first at multiplying by 10 and what we do when we multiply something by 10, 'cause we could use long multiplication to try and do this, but it's going to be really, really hard work, and it shouldn't be that confusing. Shouldn't be that hard work. So when we multiply something by 10, what we're really doing is we're making it 10 times greater. Now we know that when we make anything 10 times greater using our place value chart, it's going to move from our tens to a hundreds column or hundreds to a thousands column, it's going to move one column to the left, because it's becoming 10 times greater, okay? So you may have heard some people say things like, "Oh, just add a zero to something." And although that can be successful at times that isn't mathematically correct, and it could cause confusion later down the line. So it's better that we think of it as we're moving or the numbers, that all the numbers are becoming 10 times greater, okay? So let's have an example then. Here, we've got 35. Now, 35 in order to multiply this number by 10, I don't want to use long multiplication. I want to say actually I know that each digit is going to become 10 times greater. So I've got 30 here, if that's going to become 10 times greater, it's going to move from our tens to hundreds column. And likewise five, that's going to come 10 times greater is going to become 50, okay? So first off, we've got our tens, then we've got our ones. So then what we do now, because we've got three hundreds and five tens, but we've got no ones. So now we need to make sure that we've got our placeholder in there. So if we multiply 35 by 10, we left with 350, okay? So let's try and decimal example then. So now I've got 4.5. Now it's really important to remember that our decimal point is never going to move. That's always going to stay where it is, we can't just move back around. That needs to stay exactly where it is. So looking at our different values, well, I need to make sure that each digit in my number is going to become 10 times greater. So four is going to become 10 times greater, to become 40. And five tenths or 0.5 is going to become 10 times greater, we're going to end up with five, 'cause 0.5 times by 10 is equal to five. So I'm left with 45, I don't need a place holder this time because I don't have any space left on. So is equal to 45. Now, same principle when we multiply by a 100. It's the same thing we're doing. In this case, because we're making each digit a 100 times greater, this time we're going to have to move two places in our place value chart. Again, we're going to move to the left because they getting greater 'cause we're multiplying by 100. So let's have a look at an example. So here I've got 32 and I need multiplied by 100. Now 30 is going to multiply by 100 and it got into a hundreds, our thousands column. So we're left with 3000. And our two is going to come 10, 100 times greater, is going to move to our hundreds columns. Then I've got 3000, 200, and then I've got, well, two places which I need placeholders in, so 3,200 is my answer. Now I've gotten one more example for you with a 100. Here we've got 4.05. Now four, I'm going to multiply by 100, it's going to become 100 times greater, so I need to move it two digits in my place value chart, is going to come four hundreds. Now I still need to then think, well, this is our tens and I've got zero tenths here, but I need to make sure that I'm going to go to my ones or my hundreds. Now, what is zero tenths multiplied by 100? Well, it's still zero. There's still none of them, okay? But we need to have it there as our place value, as our place value holder, okay? Then I've got five hundredths and I need to multiply that by a 100, so it's going to go multiply by 10 multiply by 100 is equal to five. So I'm left with my answer of 405. Okay, a couple of examples of multiplying by 1000, that is going to be over to you for you to have a go. When we multiply by one 1000, you've probably already worked this out, but we're going to have to make each digit 1000 times greater. If we make something 1000 times greater, it's going to move one, two, three places to the left in our place value chart. So it's going to become a 1000 times greater. So let's have a look at an example, here we've got 43. Now, 40, if I make it a 1000 times greater is going to move to our hundreds, a thousands, our ten thousands column. So this is going to be worth 40,000. And here we've got three, it's going to move to our tens or hundreds, a thousands column, okay? So then I need to have our place value holders, so I've got three of them in this case. So I left with 43,000. Let's have a look at a decimal example, in this case 5.6. So first five, I'm going to go multiply by 10, a 100, a 1000. So again, three places to the left. So five thousands, and then one tenths is going to become a 10, a 100, a 1000 times greater. And you'll see that we can start to see a pattern of what's emerging here. So in this case, 5,600 but we need to put in our place holders to support us, okay? So 5,600. Okay, we've had a go at multiplying by 10, 100 and 1000s. Now, I'd like to give you a go to go ahead and practise that. So remembering that we've multiplied by 10, we move one place left 10 times greater, a 100, two places 'cause then we're going to a 100 times greater for each digit, and likewise for a 1000s, if we multiply by 1,000, we're going to move three places. Okay, I'm going to let you have a go. So pause the video and see if you can find the answer to this, and then when you're ready play the video. Okay, so let's have a look at some of those answers. So 45 multiplied by 10 is equal to 450, 45 multiplied by a 100 is equal 4,500, and then 45 multiplied by a 1000 is 45000. 5.67 is 56.7 multiplied by 10, multiplied by a 100 is 567 and multiplied by 1000 is 5,670. Well done if you've got that. And our decimal number slightly more confusing this one, 0.402. Now remember that zero can be a confusing. Multiply by 10, it's 4.02, multiply by a 100 is 40.2 and multiplied by a 1000 is 402. Well done, if you've got all of those. Hopefully, you're getting a hand of it now. Okay, we've learnt multiplication, now let's have a look at division. Now dividing by 10. In this case, where we are multiplying we're moving to the left because it's getting 10 times greater, this time we're going to be getting 10 times smaller if we divide by 10, okay? So if we're getting 10 times smaller, we know that we're going to be move in one place to the right, because each of these is 10 times smaller than the previous one to the right, okay? So let's have a bit of an example to prove that to us and make sure we've got good understanding. So in this case, we've got 35 and I need to divide it by 10. Remembering our decimal point, we should just make sure it doesn't move anywhere or we don't put something into it. So first off, our tens we divide it by 10, so our 30 becomes three and five ones divided by 10 become 0.5. Okay, so answer is 3.5. Okay, now I've got 4.5 here. If you want to have a go at this first before I show you, pause the video now and have a go at it and then, when you're ready play again. So 4.5 now divided by 10, remembering each digit is going to come 10 times smaller. What are you going to do? Our one first, so we're going to have four divided by 10 is equal to 0.4, and then 0.5 divided by 10 is equal to 0.05 so we're left with 0.45, okay? So now we need to put in, make sure we don't leave it as 0.45, we need to make sure we put in our place holder as 0.45 to make sure this number is that and is a proper, okay? We're done divided by 10 then, you know what's coming next. We're going to have a go at dividing by 100. So dividing by 10, moves one place to the right, then dividing by 100, it's going to move two places to the right. Think about the relationships between everything in our place value chart, okay? So we're going to be making sure that each number is going to come a 100 times smaller this time. So we're going to move two places in our place value chart. So looking at the example of 32, well first off, I'm going to make 30, going to get 10 times a 100 times smaller. So then you're left with 0.3, and then we've got point then we've got two here, so two ones, and we need to divide that by 100. So in this case, we only left with 0.02. So that gives us three tenths and two hundredths. So but now making sure we put our place holder in our decimal place and our zero placeholder, 0.32. Okay, another example for you. Dividing by 100, you may want to pause the video now and have a go and then play it when you're ready. So 40.5 in this case, making sure that we're going to move two places to the right. We're going to make every digit 100 times smaller, okay? So first off, we'll start with our tenth of 40, is going to come 10, 100 times smaller. Now zero is going to come 10, 100 times smaller, but of course it's zero so it's not going to necessarily change its value. And then we've got five tenth, it's going to become a 100 times smaller. I'm left here, I can see once I put in my decimal placeholder 0.405. Well done, if you got that guys. Okay, you know what's going to come next, dividing by 1000 this time. So just as you've noticed all the practising we've divided, multiplying by 10, a 100, a 1000, this time dividing by 10, a 100 and now a 1000, we've been moving three places to the right this time. So we're going to make every digit 1000 times smaller. Okay, let's have a look at this then. I'm not sure I'm going to have enough space in my place value chart, you might find the same. If you can, you may have to put an extra column. So starting with the number 43, let's make that a 1000 times smaller. So we start with 40 and so they get 10 times smaller, a 100 times smaller, a 1000 times smaller. And then my ones. So I've got three here, so 10, 100, a 1000 times smaller, I have three thousandths. So you can see I've got four hundredths and I've got three thousandths. Now I need to put in my place holders to make sure nothing . So I've got 0.043. So 43 divided by 1000 is equal to 0.043. Another example for you now, and I know I'm not going to have enough space for this, but we have to work out. So 5.6, if you want to pause the video and have a go at this one yourself before I go through it, then please do it. So first off, you can see, we're going to have some problems here. So I'm going to make sure I do this one first. So we need to go one, two, three places to the right. So this is going to have to be a new column now. So I'm going to have to have a new column there. We're going to have to have a ten thousandth column. Yeah, typical one to say that. So this time we've done our one, two, three, so a 1000 times smaller, and then we've got a five one. So we're going to make that 10, a 100, a 1000 times smaller as well. So then we need our placeholder, so 0.0056 or 5.6 multiplied Sorry, I'll start again. 5.6 divided by 1000 is equal to 0.0056, okay. When we get to these big numbers that can be a little bit challenging, but just remember the patterns that you're finding with these numbers and the strategy that we're using to help us solve it, and just keep talking through to make sure you've got that solid understanding. Over to you then. Pause the video now and have a go at some of these. Make sure you start and go back to that original number. It's time to divide by 10, a 100 and a 1000, and when you're ready, play the video again. So pause now. Okay guys, are we ready? So let's have a look at those answers that we came up with. So 45 divided by 10 is equal to 4.5, divided by a 100 is equal to 0.45, divide by a 1000 is equal to 0.045. 5.67 divided by 10 is equal to 0.567, divided by 100 is equal to 0.0567 and divided by 1000 is equal to 0.00567. Now 40.2, divided by 10 is equal to 4.02, divided by 100 is equal to 0.402, and divided by 1000 is equal to 0.0402. Huh, okay guys, we've made it. What I want you to do now, is you've got some task to do in your work tips, which are using and applying your knowledge of multiplying or dividing by 10, a 100 and a 1000. So we're just applying everything we've already done in the lesson. So pause the video now and then when you completed them, we'll have a look through some of those answers. Okay, so let's have a look at some of our answers then. And in that question one, was all about completing the table. So this time we're multiplying by 10, a 100 and a 1000. So we should have had 34 multiplied by 10 is equal to 340, and then we multiply that by a 100, we're left with 34000, and we multiply that by 1000, we're left with 34 million. Now in order to be able to just do the opposite, we need to be able to divide by 10. So where it comes slightly more confusing. So 67 divided by 10 is equal to 6.7, and then we multiply by 100, that's 67 multiplied by a 100 is 6700, and 6700 multiplied by a 1000 is 6,700,000. Now, a bit more challenging now because we're left with 530. We're going to have to use our knowledge of division to help us develop this part. So dividing by a 1000 'cause that's the inverse of multiplying by a 1000, we're left 0.53, then dividing this by 100, we're left 0.0053, and dividing that by 10, we could have got 0.00053. Well done if you've got those. A few more questions for you. Think about your knowledge in multiplication and division. eight multiplied by a 100, 800 10 multiply by 0.76 is 7.6. 25 divided by 100 is equal to 0.25 5.078 multiplied by 1000 is equal to 5,078, 6.78 divided by 10 is equal to 0.678, 96 multiplied by 10 is equal to 960, 7.09 divided by 100 is equal to 0.0709, and 62.06 multiplied by 100 is equal to 6,206. Now question three, circle the number that 10 times smaller than 70. You should have circled 7, and circle the number that is 100 times greater than 7.5, we could have circled 750. Well done if you got those right. And question four, some word problems for you. A box holds 10 eggs, Ronaldo buys 46 boxes of eggs, how many eggs in total does he buy? We should be in 46 multiplied by 10, so we should have got 460 eggs in total. Miss Parsons wants to buy a car and she's saving some money for it. So she saves 1000 pounds a month, how much will she have saved after 11 months? So we shouldn't have done a hundred multiply by 11, instead 11 multiply by hundreds can be a lot easier for us. And we should have ended up with 1,100 pounds saved in total. Okay, well done if you got that guys. If you've found anything a little bit challenging, then do feel free to go back and practise some of the things that we were looking at in the lesson, until you're feeling really confident about it. Okay, thank you very much for your time today guys. Please do make sure that before you go away today, you go to that end of lesson quiz and complete it. Thank you very much for your time. Hope you enjoyed the lesson and will see you again soon, bye bye.

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Multiply and Divide by 10, 100 and 1000 Including Decimal Numbers Quiz

In this lesson, we will learn the procedure for multiplying and dividing numbers by 10, 100 and 1000.

Maths

Y6 Maths

Key Stage 2

Year 6

Multiply and divide by 10, 100 and 1000 involving decimals

Multiplication and division

Number

THEME

UNIT

Represent decimal numbers in a variety of ways

Place Value to 3 Decimal Places

Multiply and divide by 10, 100 and 1000 with in context

Understand the terms 'common factor' and 'common multiple' as properties of a number

Identify properties of numbers

Multiply a decimal number by a whole number

Solve multiplication problems using known and derived facts

Use efficient strategies to multiply numbers, including decimals

Practise multiplication and division skills

Use formal written methods for short multiplication including multiplying decimals

Multiply by a two-digit number using long multiplication

Use formal written methods, including long multiplication, to solve a range of problems

Explore efficient mental strategies for division

Use the formal written method for short division

Use the formal written method of long division to solve appropriate calculations

Solve problems involving division with remainders (Part 1)

Solve problems involving division with remainders (Part 2)

Represent remainders in different ways depending on the context of the problem (Part 1)

Represent remainders in different ways depending on the context of the problem (Part 2)

Lesson overview:Multiply and divide by 10, 100 and 1000 involving decimals

Core Content

Multiplication and division: