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Hi year six.

Welcome to our third lesson in the decimals and measures unit.

Today, we'll be converting between standard units of lengths.

All you need is a pencil and piece of paper.

Pause the video and get your equipment together.

So, here's our agenda for today.

We'll be converting between standard units of length.

We'll start with a quiz to test your knowledge from our previous lesson.

Then we will recap how to multiply and divide by 10, 100 and 1,000.

We'll explore the relationship between millimetres, centimetres, and metres, and then we'll work on converting measures before you do some independent learning.

So, let's start with our initial knowledge quiz, pause the video now and complete the quiz.

Click restart once you're finished.

Good job, now we're moving on to looking at multiplying and dividing by 10, 100 and 1,000.

So, when we're multiplying a number by 10, it is becoming 10 times greater.

When we multiply by 100, it becomes 100 times greater.

And by 1,000, it becomes 1,000 times greater.

Now you may have heard, that when you multiply a number by 10, all you do is add a zero, but that is not mathematically correct.

What we're actually doing is we are moving the digits, one place to the left, so that the value of each digit becomes 10 times greater.

So, let's have a look at this together.

So, if we're multiplying by 10, we are moving the digits to the left, one place and that therefore they become 10 times greater.

So, we'll use the place value chart to help us and we'll start off with the number 35.

So, that's three tens and five ones.

If we multiply it by 10, we move each digit one place to the left.

So, this three tens moves the one place, it becomes 10 times greater so ow it's three hundreds.

The five ones becomes 10 times greater to become five tens.

And we will need a placeholder in the ones column.

So, 35 multiplied by 10 is equal to 350.

And each of those digits has moved one place to the left.

Now we'll have a look at a decimal number.

So, if I have the number 4.

5 and I'm multiplying it by 10, this is where the rule of not just adding a zero, really comes into play.

Because if I just added a zero to 4.

5, it would become 4.

50, which is actually the same as 4.

5.

So, that rule just doesn't work.

We need to move our digits.

So, we move our four one place to the left, our four ones becomes 10 times greater, so that's four tens.

Then we move our five one place to the left, our five tenths become 10 times greater, so it's five ones.

So, 4.

5 multiplied by 10 is equal to 45.

Now let's have a look at multiplying by 100.

When we multiply by 100, we move the digits two places to the left so that they become 100 times greater.

So, our digits move two places to the left, okay? And we'll have a look at that with the number 32 first.

So, we're looking at the numbers, each digit becoming a hundred times greater.

So, three tens moves one, two places to the left to become three thousands, because three tens is 30, multiply it by 100, gives us 3,000.

So, that three is now 100 times greater and the two ones moves two places to the left, into the hundreds column.

So, that's three thousands and two hundreds and we need two place holders.

So, 32 multiplied by 100 is 3,200.

Let's have a look at one using a decimal number, 4.

05.

We want to make it 100 times great, so each digit moves two places to the left.

The four ones, moves one, two into the hundreds column, the zero tenths moves into the tens column and the five hundredths moves into the ones column.

So, 4.

05 multiplied by 100 is 405.

And then finally looking at multiplying by 1,000.

When we multiply by 1,000, we want to make each digit 1,000 times greater, so we move to the left three places.

And you'll see that the number of places that we move is actually the same as the number of zeroes that each of these numbers has.

That's an easy way to help you remember.

So, let's have a look with the number 43, each digit needs to move three places to the left, one, two, three.

So, four tens becomes four, ten thousands, three ones becomes three thousands, and then we need our placeholders.

So, 43 multiplied by 1,000 is 43,000.

And our one decimal number 5.

6, each digit needs to move three pieces to the left.

One, two, three that's, five thousands, and the six moves into the hundreds column, and then we need our two place holders.

So, 5.

6 multiplied by 1,000 is 5,600.

Now we're going to recap.

Recapping dividing by 10, 100 and 1,000.

And the reason I'm going quite quickly through this is because this is a scale that I know you already know, but it's one that is essential when we're converting measures.

So, it's important that we do a quick revision of it.

So, when we divide a number by 10, it becomes 10 times smaller.

When we divide a number by 100, it becomes 100 times smaller and by 1,000, it becomes 1,000 times smaller.

So, when we were multiplying, we moved the digits to the left, but when we're dividing, we move the digits to the right.

So, when we divide by 10, we move the digits to the right one place.

And that way they become 10 times smaller.

So, we'll look with 35, three tens and five ones, each digit moves one place to the right.

So, the five ones becomes 10 times smaller and becomes five tenths because five divided by 10 is 0.

5 or five tenths.

Don't forget our decimal point.

And our three tens becomes 10 times smaller, so that's three ones.

So, 35 divided by 10 is equal to 3.

5.

Let's look at one more together, 4.

5 divided by 10, one place to the right.

The five tenths becomes 10 times smaller, so it's five hundredths and the four ones become what? Four tenths and then we need our placeholder in the ones column.

So, 4.

5 divided by 10 is equal to 0.

45.

Let's look at dividing by 100.

So, when we divide by 100, we move the digits two places to the right and that way they become 100 times smaller.

So, we'll use 32, the two ones, we move one, two places into the hundredths column.

And the three tens, we move into the tenths column and we need a place holder.

So, 32 divided by 100 is equal to 0.

32.

And then let's have a look with a decimal.

So, we'll go for 0.

405.

We move everything two places to the right.

So, that the four will move into the hundredths column, the zero will move into the thousandths column and the five will move into the ten thousandths column.

And we need to have our place holders in the tenths and the ones column.

So, 4.

05 divided by 100 is equal to 0.

0405.

And then finally dividing by 1,000, where we're making the number a thousand times smaller.

So, we're moving it to the right, three places this time.

And we'll have a look at this first of all, with the number 43.

Each digit moves three places to the right.

Three moves one, two, three into the thousandths.

Three divided by 1,000 is three thousandths and four moves into the hundredths column.

And then remember that we must have a place holder in the tenths, we have a decimal and we have a placeholder in our ones.

And then one more example, 5.

6.

So, we're moving everything three spaces to the right.

The five ones moves one, two, three into the thousandths.

We didn't think this through because it's going to go on where I've written already.

The six tenths is going to move this column into the ten thousandths and then we need our placeholders in our ones, tenths and hundredths.

So, 5.

6 divided by 100 is equal to 0.

0056.

Now it's your turn for some quick revision.

So, I'd like you to pause the video and practise multiplying by 10, 100 and 1,000.

Each time go back to the original number.

So, you'll do 45 times 10, 45 times 100 and 45 times 1,000.

And you can use a place value column if you need to.

So, 45 times 10, we were moving the digits one space to the left.

So, that would become 450, that's 10 times greater.

Timesing by 100, we're moving the digits two places to the left, so that became 4,500, that's 100 times greater and multiplying by 1,000, three places to the left.

So, that's 45,000.

Now moving on to the next one, which was a decimal 5.

67.

We move one space to the left, which became 56.

7.

Then two spaces, 567, and then three, 5,670.

And the last one, we move one space in the left to become 4.

02, and then two spaces, 40.

2, and then finally 402.

So, it is really important now where perhaps you used to think that adding on a zero was the best way to multiply by 10, 100 and 1,000, it just doesn't work for decimal numbers.

So, it's best to think about moving the digits.

Now your turn to pause and have a go at dividing by 10, 100 and 1,000.

And again, go back to the original number each time.

45 divided by 10, 45 divided by 100, 45 divided by 1,000.

Pause the video now and complete the table.

So, 45 divided by 10, you move the digits one space to the right.

So, it will become 4.

5.

Then two spaces to the right will be 0.

45, and three spaces to the right will be 0.

045.

5.

67, the first one divided by 10, 10 times smaller is 0.

567.

100 times smaller is 0.

0567, and 1,000 times smaller is 0.

00567.

And the final one 40.

2 divided by 10 is 4.

02.

Divided by 100, is 0.

402 and divided by 1,000 is 0.

0402.

Now let's apply this to measure.

So, we're going to explore the relationship between millimetres, centimetres and metres.

So, first of all, having a look at a ruler, I want you to think about what you can say about the relationship between millimetres and centimetres.

Pause the video now and make some notes.

So, things that you may have noted using a ruler to help you, is that one centimetre is equivalent to 10 millimetres or 10 millimetres in one centimetre.

So, you may also have noticed that 1/10 of a centimetre is equal to one millimetre and therefore 0.

1 centimetres is equal to one millimetre.

You may have also said things like, a centimetre is 10 times greater than a millimetre or a millimetre is 10 times smaller than a centimetre.

So, if we know that 10 millimetres is equal to one centimetre, how can we convert between millimetres and centimetres? So, 10 millimetres is equal to one centimetre to get from millimetres to centimetres, we have to divide by 10 and to get from centimetres to millimetres, we have to multiply by 10.

And we'll explore this more in a minute.

Now we're going to look at the relationship between centimetres and metres.

So, make some notes about this relationship like we did for the last relationship.

So, you may have noticed looking at the metre stick, that one metre is equal to 100 centimetres.

There are 100 centimetres in one metre.

You might have said that therefore, 1/100 of a metre is equal to one centimetre or 0.

01 metres is equal to one centimetre or a metre is 100 times greater than a centimetre or a centimetre, 100 times smaller than a metre.

So, therefore, if we knew that there are 100 centimetres in a metre, I want to know how many millimetres there are in one metre.

Well, let's have a look at this on our next slide all together.

So, we know that one metre is equal to 100 centimetres, so we need to think about how do we convert from metres to centimetres? How do we get from one to 100? Well, we multiply by 100.

So, to convert from metres to centimetres, we multiply by 100.

Now, if we know that there are 10 millimetres in one centimetre, we know that there are 1,000 millimetres in 100 centimetres.

To convert from centimetres to millimetres, we already looked at this relationship, we multiply it by 10.

Remember, one centimetre is 10 millimetres.

So, the relationship there is multiplied by 10.

So, my last question was, how many millimetres are that in one metre? Remember the prefix milli meant 1,000.

So, a millimetre is 1,000 of a metre, so there are 1,000 millimetres in one metre.

To convert from metres to millimetres, we multiply by 1,000.

And you can see that we could do it in two steps.

We could convert to centimetres, then to millimetres by multiplying by 100 and then 10.

Or we can do it in one big jump by multiplying by 1,000.

Now let's have a look at the inverse relationship.

So, how do I convert from millimetres to centimetres? Well, I divide by 10.

Centimetres to metres, I divide by 100.

So, now can you think about the big jump from millimetres to metres? I would divide by 1,000.

So, we'll keep that that to help us with our conversion of some measures, okay? So, here we have a helpful conversion table at the top, and I want to know what is 4,500 millimetres in metres? Now I know that there are 1,000 millimetres, looking at my conversion up here, there are 1,000 millimetres in one metre.

So, if I want to convert from millimetres to metres, I need to divide by 1,000, divide by 10 and divide by 100.

So, I'm looking at 4,500 millimetres divided by 1,000.

And that will give me my answer in metres, the equivalent in metres, okay? So, I'll use my place value chart to help me.

So, I'm going to have my thousands, hundreds, tens ones.

I know this is going to become a decimal number because I'm dividing, so I'll put my tenths, hundredths, and then I'll put my number 4,500.

If I'm dividing by 1,000, I'm moving, three to the right.

So, I'm going to need another column, I've just realised that.

So, I made this one, two, three here, this one, move one, two, three to here, the five moves one, two, three into the tenths and the four moves one, two, three here.

Now these zeroes here are not necessary because they're not holding the place of anything.

So, my answer is just 4.

5.

So, 4,500 millimetres is equivalent to 4.

5 metres.

Let's do another one together.

So, this time I'm converting from metres into millimetres.

So, from metres to millimetres, one metre is 1,000 millimetres.

So, that big jump is multiplying by 1,000.

So, I'm going to be doing 5.

6 times 1,000.

If I multiply by 1,000, I'm moving three to the left, so I'll put my quick place value chart up.

So, I have my ones, decimal point and my tenths.

I know I don't need to go any further to the right because I'm multiplying, so I'm moving my digits left.

So, I'll just put in tens, hundreds and thousands and I'll stop there.

So, I'm multiplying 5.

6 by 1,000.

So, my five is moving three places to the left, one, two, three.

My six moves one, two, three, and then I need two place holders here.

So, 5.

6, multiply by 1,000 is equal to 5,600 millimetres,.

So, 5.

6 metres is equal to 5,600 millimetres.

Now it's your turn.

You've got your helpful conversion chart below.

I'd like you to work out what four centimetres is in metres, 95 metres in millimetres and 9.

5 centimetres in millimetres.

Pause the video now and work out the conversions.

So, centimetres to metres, we can say you divide by 100.

So, four centimetres divided by 100 is equal to 0.

04 metres.

Always remember to put your units as well.

95 metres in millimetres, to convert from metres to millimetres, we multiply by 1,000.

95 multiplied by a thousand is 95,000 millimetres.

And then the last one, centimetres in millimetres.

I can see that I multiply by 10, 9.

5 centimetres is equivalent to 95 millimetres.

Now let's have a look at kilometres.

So, kilo means thousands, one kilometre is 1,000 metres and one metre is 0.

001 kilometres or 1/1,0000 of a kilometre.

So, using this, how do I convert from kilometres to metres? If one kilometre is 1,000 metres, how do I convert? So, I convert by multiplying by 1,000.

One kilometre is to 1,000 metres, and to convert from metres to kilometres, I divide by a 1,000.

So, let's look at the first one together.

5.

6 kilometres in metres.

To go from kilometres to metre, I multiply by 1,000.

So, I'll be, I'm being asked here to do 5.

7, I think I said 5.

6, 5.

7 kilometres to metres, 5.

7 multiplied by 1,000.

I move the digits three places to the left.

And that is equal to 5,700 metres.

I'd like you to do this one independently.

So, pause the video now and calculate 4.

5 kilometres in metres.

So, kilometres to metres, you are multiplying by 1,000.

4.

5 times 1,000 is equal to 4,500 metres.

Let's convert the other way.

So, the first one we'll do together.

What is 467 metres in kilometres? Metres to kilometres is divide by 1,000.

So, 467 divided by 1,000.

I moved my digits three places to the right, which will be 0.

467 kilometres.

Now pause the video and calculate 5362.

45 metres in kilometres.

So, you are multiplying 5362.

45, so you are dividing that by 1,000 to move from metres into kilometres, therefore you are moving your digits three places to the right, which means that 5.

36245 kilometres is equal to 5,362.

45 metres.

Now it's time for you to compete some independent learning.

So, pause the video and complete the tasks and then click restart once you're finished.

So, for question one, you were asked to complete the table by multiplying by 10, 100 and 1,000.

But for some of them you needed to use the inverse, dividing by 1,000, dividing by 100, and dividing by 10.

So, we'll start with the first one.

34 multiplied by 10 is 340.

340 multiplied by 100 is 34,000.

And 34,000 multiplied by 1,000, is 34 million.

Onto the next one 67.

We had to use the inverse to go back one, 67 divided by 10 is 6.

7.

And then back in the right direction, 67 multiplied by 10 is 6,700 and 6,700 multiplied by 1,000 is 6, 700,000.

And then for the last one, we were working in reverse the whole time using the inverse.

So, 530 divided by 1,000 is 0.

53.

0.

53 divided by 100 is 0.

0053 and divided by 10 is 0.

00053.

Onto question two, here you were asked to fill in the gaps.

So, starting here with converting from metres to centimetres, you multiply by 100, from centimetres to millimetres, you multiply by 10, and then the overarching metres to millimetres, you multiply by 1,000.

Then looking at the inverse relationship, millimetres centimetres, you're dividing by 10, centimetres to metres, you're dividing by 100, and millimetres to metres, you're dividing by 1,000.

The question three, you were asked match the equivalent measures, where there was one odd one out.

So, we worked systematically.

We can see that four centimetres is equivalent to 40 millimetres, which is also equivalent to 0.

04 metres.

And then 0.

095 metres was equivalent to 95 millimetres and also to 9.

5 centimetres.

And then moving on 95,000 millimetres.

This is a squiggle, was equivalent to 95 metres and also 9,500 centimetres.

And finally 0.

4 kilometres was equivalent to 400 metres, which meant that the odd one out was four kilometres that didn't join up with anything else in the table.

So, for question four, this is a multi-step problem.

The distance from Cambridge to Oxford is approximately 135 kilometres.

The distance from Edinburgh to Glasgow is approximately 75 kilometres.

So, you were, first of all asked, how much further is Cambridge to Oxford, than Edinburgh to Glasgow and then asked to give your answer in metres.

So, we find the difference between the two distances, 135 kilometres subtract 75 kilometres is equal to 60 kilometres.

And then you were asked to give that answer in metres.

So, we're converting 60 kilometres into its equivalent metres.

We know that to convert from kilometres to metres, we multiply by 1,000.

So, 60 kilometres is equal to 60,000 metres.

And your final question.

So, as part of my training a 10K race in July, that's 10 kilometres, I've been increasing the amounts I run each day over the last week.

So, on Monday, I ran 4.

65 kilometres.

Each day, I added 375 metres to that distance.

So, I'm adding the same each day.

So, what I'm creating here is a linear sequence.

Now I'm asked, how far did I run on Sunday in kilometres? What I'm going to do first is I want to have these in the same units, so that it's easier to add.

So, I'll convert kilometres to metres by multiplying by 1,000.

So, on Monday I ran 4.

65 kilometres, which is the same as 4,650 metres.

So, Monday 4,650 metres, on Tuesday an extra 375 metres.

So, I did 4,650 plus 375 metres, which equals 5,025 metres.

On Wednesday, I did another 375 on top of that.

So, I did 5,025 plus 375, is equal to 5,400.

Then on Thursday, I did the same as Wednesday, but I added another 375, which equals to 5,775 metres.

On Friday, I did 5,775 and I added another 375, which equals 6,150 metres.

On Saturday, I did my 6,150 metres, and I added another 375, which is equal to 6,525 metres.

And then on Sunday, which is my last day, I did my 6,525, and I added my 375, which is equal to 6,900.

So, on Sunday I ran 6,900 metres and I'm being asked for my answer in kilometres, metres to kilometres.

I divide by 1,000.

So, my answer was 6.

9 kilometres run on Sunday.

Great work today year six.

In our next lesson, we will be solving problems involving the conversion of length.

I'll see you then.