Lesson video

Hi.

Welcome to today's lesson.

My name's Mr. Peters.

And in this lesson today, we're gonna be thinking about another really important example of rounding with decimal numbers.

We're gonna be thinking about rounding decimal numbers with hundredths to the nearest whole number.

Once again, we use this skill a lot in our daily lives, so it's definitely worth us taking the time here to have a think about how we can use this for ourselves and what we do.

When you're ready, let's get started.

So, by the end of today's lesson, you should be able to say that you can round decimal numbers with hundredths to the nearest whole number.

Throughout this lesson, we're gonna have a number of key terms for us to think about.

I'm gonna have a go at saying them first, and then you can repeat them afterwards.

Are you ready? My turn: multiple.

Your turn.

My turn: previous.

Your turn.

My turn: next.

Your turn.

My turn: rounding.

Your turn.

So when we think about what a multiple is, a multiple is the result of multiplying a number by an integer.

For example, 2 multiplied by 5 is equal to 10.

So 10 is a multiple of both 2 and 5.

When we think about the word previous, something that comes before something else can be known as the previous thing, and therefore something that comes after something else can also be known as the next thing.

And finally, rounding, rounding is a process we use to make a number more simple.

However, it still keeps the number close to the value that it had originally.

In our lesson today, we're gonna break our learning down into two cycles.

The first cycle, we'll think about rounding hundredths to the nearest whole number.

And the second cycle, we'll think about rounding in different contexts.

Let's get started.

In this lesson today, you will meet four of our characters, Izzy, Sam, Laura, and Andeep.

And they're gonna share a lot of their thinking throughout the lesson.

So Izzy and her class are recording how long it takes everybody to run 50 metres.

They've decided that they want to round each one of the times in the table to the nearest second.

Have a look at the times on the right-hand side.

Izzy's suggesting we start with her time.

Her time was 7.

49 seconds.

Have a look at our number line and see where 7.

49 has been placed.

Hmm, that's right.

What are the previous and next multiples of one second that 7.

49 is between? Well, we can say that 7.

49 is between 7 and 8 seconds.

7 is the previous multiple of one second, and 8 is the next multiple of one second.

Let's look at this in a bit more detail.

We can see here that 7.

49 is 49 hundredths of a second away from 7 seconds.

And we can also see that 7.

49 is 51 hundredths of a second away from 8.

Therefore, 7.

49 rounded to the nearest multiple of one second would be 7.

We can record that in our table just like this.

Let's have a look at Sam's time then.

This time, Sam had a time of 7.

51 seconds.

Hmm, let's have a think about how we'd record this using the stem sentence below.

Well, 7.

51 seconds is between 7 seconds and 8 seconds again.

7 is the previous multiple of one second, and 8 is the next multiple of one second.

Let's have another closer look.

We know that 7.

51 is going to be 51 hundredths of a second away from 7.

And we also know it's gonna be 49 hundredths of a second away from 8.

Therefore, which multiple of one second is it closest to 8? That's right, 7.

51 rounded to the nearest multiple of one second would be 8 seconds.

Again, we can record that in our table like so.

Sam's saying, "Hang on a second.

We finished our race really close to one another.

However, your score rounds to a lower time than my score, and it looks like you ran it a lot faster than I did." That doesn't seem to be fair.

Let's have a look at a bit more detail here.

7.

49, which was Izzy's time, was 49 hundredths of a second away from 7.

And 7.

51, which was Sam's time, was 49 hundredths of a second away from 8.

So we can see that actually this rounding is correct.

Izzy's time was closer to 7, and Sam's time was closer to 8.

And so Laura is now pointing out, well, anything with 49 hundredths or less will round to the previous multiple of one second.

And anything with 51 hundredths or more will round to the next multiple of one second.

Andeep's saying, "Well, what if our time had 50 hundredths of a second?" Let's have a look.

Andeep's saying that because his time did have 50 hundredths of a second.

His time was 8.

50.

Let's think about how we can round this then.

8.

50 is between 8 and 9 seconds.

8 is the previous multiple of one second, and 9 is the next multiple of one second.

We can see that it is 50 hundredths away from 8, and we can see that is also 50 hundredths away from 9.

And in these examples, where a number is exactly in the middle between two multiples of one, then we would round to the next multiple of one.

So 8.

50, or 8 seconds and 50 hundredths of a second, rounded to the nearest one second would be 9 seconds.

Izzy's now recording this in our table.

And Andeep says, "Well, funnily enough, I preferred the original time I had," 'cause now his time has rounded up, hasn't it, to 9 seconds, when before he had 8.

5 seconds.

Laura says, "Okay, now it's my time to round." Have a look at Laura's number.

Can you have a think about that stem sentence that we had? Could you articulate how we could identify the previous and next multiples of one second? That's right.

6.

92 is between 6 and 7 seconds.

6.

92 has 92 hundredths.

So we round to the next multiple of one second.

So, therefore, 6.

92 would round to 7 seconds.

Okay.

Izzy now places that into our table again.

And Laura's now got a question.

She's saying, "Well, hang on a minute here.

I beat you in the race, Izzy, whereas both our times are now rounded to the same second, hasn't it? Therefore we can't tell who won the race." Let's have a look about what Laura is referring to.

Laura's time was 6.

92.

It's only 8 hundredths of a second away from 7.

So it would round to the next multiple of one second, which would be 7.

And then if we extend our number line, we can put Izzy's time on of 7.

49, and we can see that Izzy's time is 49 hundredths of a second away from 7, but it would be 51 hundredths of a second away from 8.

So it's closer to 7.

So 7.

49 would also round to 7 seconds to the nearest one second.

So as we can see, both of these numbers are closest to 7 than any other whole number on our number line.

Laura's now pointing out, she thinks that the way that we've rounded these numbers here aren't really helpful to see who the fastest runners were.

Izzy's saying it doesn't matter about the fastest times for today.

What matters is thinking about the groups of the runners that we're gonna put the children into.

So when they race next, they'll all have the best opportunity to be as competitive as they can be, to get as close as they can to winning the race.

And finally, Sam points out that she feels that some of the runners will feel a lot happier with the scores than others will.

Sam's now asking, "Well, what other runners might be happier with their time than other people?" Let's have a look.

Izzy's now saying, "I wonder if we could do this without actually having to draw a number line." Let's think back to some of our previous learning so far.

Izzy said that she noticed that the hundredths digit doesn't matter when rounding to the nearest whole second.

Laura's a little bit unsure, and she's asking, "What do you mean?" Well, let's take Izzy's time for example.

Izzy's time was 7.

49 seconds, and this is rounded to 7 seconds.

Her time had 49 hundredths of a second.

And if we ever look at the tenths digit, the tenths digit is a 4.

Izzy thinks that any number with tenths that are either 0 tenths, 1 tenth, 2 tenths, 3 tenths, or 4 tenths would round to the previous multiple of one second.

So Izzy's time, 7.

49, has 4 tenths, so it would round to the previous multiple of one second, which would be 7.

Let's take a look at Sam's score.

Sam score was recorded at 7.

51.

If we look at the tenths digit, Sam has 5 tenths of a second, and therefore any number with 5 tenths or more, so it could be 5 tenths, 6 tenths, 7 tenths, 8 tenths, or 9 tenths, any of these would round to the next multiple of one second.

Let's look at this on our number line.

Any of these numbers here, for example, all the way up to 0.

49, would round to the previous multiple of one.

Whereas any of these numbers, for example, all the way up to one whole, would round to the next multiple of one second.

And in this case, that would be 1.

So let's now use this to help us when thinking about rounding Aisha and Jacob's time.

Aisha's time is 8.

90.

Her number is between 8 and 9 seconds.

And her number has 9 tenths, so this would round to the next multiple of one second.

We know her time was between 8 and 9, therefore the next multiple of one second would be 9 seconds.

Let's have a look at Jacob's time.

Jacob's time is 8.

02.

It's between 8 and 9 seconds again.

However, he actually has 0 tenths in the tenths column.

Therefore, it would round to the previous multiple of one second.

In that case, Jacob's time would round to 8.

Izzy's asking, "Well, who might be happy this time with their rounded time?" Well, Aisha's time rounded up to 9, didn't it? And Jacob's time rounded down to 8.

So I've got a feeling that Jacob might be marginally happier that he has a slightly quicker time this time.

Okay, time for you to check your understanding now.

5.

49 rounded to the nearest one second is A, B, C, or D.

Take a moment to have a think.

That's right.

5.

49 rounded to the nearest one is 5.

And another check, which numbers round to 3 as the nearest multiple of one, A, B, C, or D? That's right.

It's both A and B.

How do we know that? Well, we can see that A has 0 tenths in the tenths column.

Therefore, it would round down to the previous multiple, in that case 3.

And 2.

75 has 7 tenths, which would round up to the next multiple of one.

And in that case, that would also be 3.

Okay, and on to task one for today, what I'd like to do is have a go at filling in the missing numbers.

Good luck, and I'll see you back here shortly.

Okay, let's go through these together then.

4.

2 rounded to the nearest multiple of one is 4.

4.

25 round as the nearest multiple of one is also 4.

4.

52, hmm, I have to think carefully there.

Those digits have switched round, haven't they? 4.

52 has 5 tenths, doesn't it? Therefore, it would round to the next multiple of one, which would be 5.

5.

42, hmm, well, that's between 5 and 6, and it has 4 tenths, and that would round to the previous multiple of one, so that would be also 5.

2.

45 would round to the previous multiple of one, which would be 2.

Notice this time how the number has got bigger, that 12.

45 is between 12 and 13.

It has 4 tenths, so it would round to the previous multiple of one, which would be 12.

And look, our numbers got even bigger again, 120.

45.

Well 120.

45 is between 120 and 121.

It has 4 tenths, so it would round to the previous multiple of one.

So it would be 120.

And then, finally, 120.

54, hmm, well, again, this is between 120 and 121.

However, this time, it's got 5 tenths.

So that would round to the next multiple of one, which would be 120.

Well done, if you managed to get all of those.

Okay, let's move on to cycle two of our lesson now, rounding in different contexts.

So we're gonna start thinking about how we can go about buying carpets.

Carpets can be measured in different lengths.

And when a customer asks for a carpet, they can either ask for the length of their carpet to be to the nearest 10 metres, to the nearest one metre, or to the nearest one tenth of a metre.

So we're gonna start thinking about the carpet lengths that a customer could ask for.

Let's have a look at our first carpet.

Our first carpet, the colour of it is Earl Grey.

And the customer is looking for a length of 12.

35 metres long.

Let's see what they can actually ask for.

So to the nearest 10 metres then, well, 12.

35 is between 10 metres and 20 metres.

And we can see that here on our number line.

10 and 20 are multiples of 10 metres, aren't they? So we can see that we've got the 10 metres on the left-hand side, and 20 metres on the right-hand side.

The arrow is pointing to where 12.

35 would sit on our number line.

And we can see that 12.

35 metres rounded to nearest 10 metres would be exactly 10 metres.

So we can record that in our table then.

If a customer wanted to buy this carpet to nearest 10 metres, they could buy a length of 10 metres.

Let's have a look to the nearest metre now.

12.

35 to the nearest metre is between 12 metres and 13 metres.

And we can see that again on our number line.

We've placed where 12.

35 would sit on our number line.

And, again, we can see that 12.

35 would indeed be closer to 12 metres.

So we could say that 12.

35 rounded to the nearest one metre would be 12 metres.

And, again, we can place that in our table like so.

And, finally, 12.

35 to the nearest one tenth of a metre, well, 12.

35 is between 12.

3 and 12.

4.

12.

35 would sit exactly in the middle of 12.

3 and 12.

4.

So, therefore, it would round to the next multiple of one tenth, which would be 12.

4.

We can place that on our table like so.

So have a little think.

We've just rounded to the nearest 10 metres, to the nearest one metre, and to the nearest tenth of a metre.

And I'm asking you now, which digit did you have to focus on each time when rounding to each of those different values? Well, when rounding 12.

35 to the nearest 10 metres, it was the ones digit we had to look at, didn't we? The ones digit told us whether it was closer to 10 metres or 20 metres.

And because the ones digit was a 2, that meant it was closer to 10 metres than 20 metres.

So, therefore, 12.

35 rounded to the nearest 10 metres was 10 metres.

Let's have a look at the next one, 12.

35 rounded to the nearest metre.

Well, when we were rounding to the nearest metre, we knew that it would be between 12 and 13 metres.

So we had to look at the tenths digit to tell us how far along the number line it would sit between 12 and 13.

The tenths digit is a 3 here, so we know it's gonna be closer to 12 than to 13.

So 12.

35 rounded to the nearest one metre is 12 metres.

And then, finally, when we were rounding to the nearest tenth of a metre, it was, in fact, the hundredths that we had to have a look at, wasn't it? We know that 12.

35 is between 12.

3 and 12.

4.

And, again, we had to look at the hundredths digit to tell us how far along the number line it sat between 12.

3 and 12.

4.

We know it sits exactly halfway between these two multiples, and therefore, when it does sit exactly halfway, it rounds to the next multiple.

And in this case, it rounds to the next multiple of one tenth, so it would round to 12.

4 metres.

So, at this point, Sam's noticed something really, really important, and I wonder if you've noticed it, too.

Take a moment to have a think for yourself.

Sam's thinking that the important digit that helps us when we're thinking about rounding is the digit to the right-hand side of the place value that we want to round to.

Have a look at the numbers on the left.

The number in green tells us the value that we wanted to round to, and the arrow points at the digit we had to look at to help us with that.

So, in the first example, we wanted to round to multiples of 10, and therefore we had to look at the ones column.

In the second example, we wanted to round to multiples of one, but we had to look at the tenths column.

And in the last example, we wanted to round to multiples of one tenth, but we had to look at the hundredths column.

Hmm, that's a really useful generalisation to help us when we're thinking about rounding.

So I wonder if we can use this generalisation now to help us with some different contexts.

The vet likes to record the rabbit's weight to the nearest gramme.

What would the weight of the rabbit be to the nearest gramme? Well, we can see that the weight of the rabbit is 80.

72 grammes.

And Sam has put an arrow pointing at the ones column, because this is what we want to round to.

We want to round to the nearest gramme.

We know that 80.

72 is between 80 grammes and 81 grammes, and therefore, if we want to round to the nearest gramme, we actually have to look at the column to the right-hand side to round to the nearest gramme.

So we've got 80.

72, and now we're looking at the 7 tenths of a gramme, aren't we? 7 tenths is greater than 5 tenths, so it would round to the next multiple of one gramme.

So, therefore, 80.

72 rounded to the nearest multiple of one, or to the nearest gramme, would be 81 grammes.

Well done, if you managed to figure that.

Okay, time for you to check your understanding now.

To help you round, you look at the column to the left of the place value that you want to round to.

Take a moment to have a think.

That's right.

It's false, isn't it? Have a look at these justifications.

Which one of these helps you to support that? Yep.

It's A, isn't it? You look at the column to the right of the place value you want to round to in order to help you round.

And another check, when rounding to the nearest multiple of one, you look at the something digit.

Is it A, B, or C? That's right.

It's B, isn't it? When rounding to the nearest multiple of one, you look at the tenths digit, don't you, in the tenths column, to help you identify whether to round to the previous or next multiple.

Okay, onto our final practise task for today then.

What I'd like you to do is have a go at completing these questions here, thinking about rounding in different contexts.

And then what I'd like you to do as well is go back to our carpet example from earlier on and have a think about these different carpets and their lengths and what measurements we could offer to customers for the nearest 10 metres, to the nearest one metre, and to nearest one tenth of a metre.

Good luck with that, and I'll see you back here shortly.

Okay, let's go through this then.

Jacob is selling bags of apples, and he prices the bags of apples to the nearest one kilogramme.

So for 1 kilogramme, it'll cost you 1 pound 80.

For 2 kilogrammes, it'll cost you 2 pounds 40.

And for 3 kilogrammes, it'll cost you 3 pounds 60.

One of the bags of apples that he has weighs 2.

45 kilogrammes.

So how much would it cost to buy this bag of apples? Well, we want to round 2.

45 kilogrammes to the nearest kilogramme, or to the nearest one kilogramme.

Therefore, we need to look at the column to the right-hand side of the ones column, don't we? In this case, we have 4 tenths.

So 4 tenths is less than 5 tenths.

so it would round to the previous multiple of one, and in that case, it would be 2 kilogrammes.

So to buy this bag of apples, you would have to pay 2 pounds 40 as the price of a 2-kilogram bag of apples is 2 pounds 40.

For question two, Sam is drinking from a 3-liter bottle of water.

She drinks 0.

72 litres of water.

How much does she have left to the nearest litre? Well, if Sam has drunk 0.

72 litres, that means she has remaining 2.

28 litres of water.

2.

28 litres of water is between 2 litres and 3 litres.

And if we want to round to the nearest 1 litre, then we also need to look at the column to the right of the ones, which would be the tenths again.

And 2.

28 litres, the tenths digit is a 2.

Therefore, it would round to the previous multiple of one.

So we can say that Sam roughly has 2 litres of water remaining in her bottle.

And then, finally, our remaining task here, working out the lengths that we could sell our carpet for, the colour Moon Hue could be sold at a length of either 30 metres to the nearest 10 metres, 27 metres to the nearest one metre, or 27.

1 metres to the nearest one tenth of a metre.

Sandy Pebble could be sold for either 40 metres to the nearest 10 metres, 36 metres to the nearest one metre, or 36.

4 metres to the nearest one tenth of a metre.

And, finally, Forest Vert could be sold to the nearest 10 metres at 100 metres.

It could be sold for 100 metres to the nearest one metre.

And it could also be sold for 100 metres to the nearest one tenth of a metre.

Hmm, isn't it interesting how a number, when rounded to the nearest 10, one, or one tenth could have the same value for each one of those? Well done, if you managed to get all of that.

Okay, that concludes our learning for today.

Hopefully you've enjoyed it, and hopefully you're feeling a lot more confident at rounding decimal numbers with hundredths to the nearest whole number.

So to summarise our thinking for today, decimal numbers with hundredths can be rounded to the nearest whole number by focusing on the tenths digit.

And, also, when we're looking to round, we can look at the digit to the right of the place value that we want to round to, to help us identify whether to round to the previous or next multiple.

Thanks for joining me today.

I've really enjoyed myself.

Hopefully you have, too, and I'll see you again soon.

Take care.