Lesson video

Hi there, my name's Ms. Lambell.

You've made such a super fantastic choice, deciding to join me today and do some maths.

Come on, let's get started.

Welcome to today's lesson.

The title of today's lesson is Rounding to Three Decimal Places and that's within the unit Estimation and Rounding.

By the end of today's lesson, you will be able to round numbers to three decimal places.

A quick reminder about what we mean in maths when we say round is when we change a number to another number that is approximately the same value but it's easier to work with.

So an example there would be to round 561 to the nearest 10 would be 560.

Today's lesson is split into two learning cycles.

In the first one we are going to have a look at representing decimals on a number line.

You'll be really familiar with number lines and even previously you may have considered writing different decimals on number lines.

And then we'll move into actually rounding to three decimal places and how we're going to do that without a number line.

Let's get going on that first learning cycle.

So remember here we're going to concentrate on using number lines.

I'd like you to write down for me on a piece of paper or a mini whiteboard, a number that fits on this number line.

It has to therefore be between two and three.

Write one down for me.

You probably haven't got exactly the same as I've got here, but here are some examples of some things that you may have.

2.

1, 2.

56, 2.

8.

Basically as long as your number starts with two and has a decimal point directly after the two, then your answer is going to be correct.

What about if I zoom in on my number line and now I ask you to write me down something that's between 2.

5 and three? Go on, give it a go.

What have you got? These are some examples of things you might have, 2.

6, 2.

73, 2.

9.

As long as you have something starting with 2.

5 or 2.

6, seven, eight or nine, then your answer is going to be correct.

Now let's zoom in again.

What about if I ask you to write down a number that's between 2.

9 and three? Go on, give it a go.

And here are some examples, 2.

93, 2.

956, 2.

9708.

Here, as long as your answer starts with 2.

9 and then something, then your answer is correct.

And this one, could you write me down a number that is between 2.

95 and three so that it would fit onto this number line? Examples here, 2.

951, 2.

956, 2.

9708.

As long as it starts with 2.

95, 2.

96, 2.

97, 2.

98 or 2.

99, then you've got a correct answer.

Now we are gonna start looking at a specific point on our number line 'cause that's going to help us as we move forward with actually rounding to decimal places when we are using a number line.

The arrow is pointing to the midpoint of the number line.

The midpoint remember, means the point that is exactly halfway between.

What number is the arrow pointing to? What number is halfway between two and three? That's another way to think of this question and I know you can tell me what number is between two and three, but remember this time exactly halfway between.

I've written it there as 2.

5.

Remember today's lesson is all about decimals.

You may have written two and a half there and that would be fine because I didn't specify, did I? To start with, that I'd like your answer as a decimal, but from now on please give me all your answers as decimals.

Notice this time there's no EG.

There is only one point that is exactly halfway between two and three, only one acceptable answer here.

If it's not obvious, however, a really neat trick for finding halfway between two numbers is to half the sum of those two numbers.

So we've got here two and three, so we're gonna sum those.

Remember sum means add together, and then we're gonna half it.

Two add three is five, divided by two, we can see it's 2.

5.

So if the numbers, if it's not immediately obvious, remember that you can sum those two numbers and then find half of it.

What is the arrow pointing to now? Remember it's the midpoint.

I'll give you a moment to come up with your answer to that.

If it's not obvious, remember, we're gonna sum the two numbers and then we're going to find half of that.

So 2.

5 add 2.

6 divided by two is 5.

1 divided by two.

So it was 2.

55, did you get that? Great work, what about these two? Can you please tell me what number the arrow is pointing to now? Again, you may have chosen to find the sum of them and half it, the sum of those is 5.

11, divided by two is 2.

555.

The midpoint of 2.

55 and 2.

56 is 2.

555.

And this one, now you may have spotted something now that might help you in future to do this quickly, but remember I want you to understand why.

And this time it was 2.

5555.

Well done if you've got all of those right.

The key thing here to remember is, is if you are not sure, add together the two values and then find half of that.

We're now going to look at how that can help us round to three decimal places on our number line.

We're going to round 0.

5672 to three decimal places.

We need to identify the numbers to three decimal places either side of 0.

5672.

You should be familiar with having done this previously with things like rounding to the nearest 10 or rounding to the nearest 1,000 or whole number or even maybe some with one decimal place and two decimal places.

Let's have a look at the digit that is in the third decimal place and that's a seven.

So we count from the decimal point and we go to the third column, which in this case is the thousandths column.

We use this as our lower value on our number line, 0.

567.

This value, we need to increase the thousandths digit by one, giving us 0.

568.

Now you'll be able to see why I asked you to find all of those midpoints.

We now need to know what is halfway between those two.

Find the halfway point, that's what we need to do and that is 0.

5675.

Let's take a look at our number, it was 0.

5672.

So if we put that on our number line, remember it doesn't need to be exact.

All I need to do really is decide is it going to the left of the midpoint or to the right of the midpoint.

And here we can see it's to the left, so it is closer to the lower value.

0.

5672 is equal to 0.

567 and that's to three decimal places.

Let's try another.

We need to identify the numbers that are gonna go either end of our number line, this time the zero is in my third decimal place, so that is going to be my lower value.

Don't forget, we still need the 0.

34 and then the zero, and then this is going to be increasing the thousandths digit by one, 0.

341.

We're gonna find that halfway point, which we're expert at now.

So I have gone through that quickly, but if you need to go back and recap how to find the midpoint, you could do that.

You could pause the video and go back and watch that bit again.

Now let's place our number.

And again, it doesn't need to be exactly, we just need to identify is it going to be to the left or to the right.

And this time we can see that it rounds to the higher of those two values on our number line.

0.

34081 is 0.

341 to three decimal places.

And another one, we should be good at this now.

So we identify the digit in the third decimal place, that gives us our lower value, our upper value is where we increase the thousandths digit by one, which is 12.

040.

We find the halfway point.

Then we place our decimal onto there and we can see it's very, very, very slightly larger than the midpoint.

So that means we're going to round it up to the higher of the two values.

So it rounds to 12.

040.

Remember we need the zero in that third decimal place because the question said to three decimal places.

We don't want it to look like we've just forgotten to include that.

We'll do one together on the left and then you can have a go on the right independently and then you'll be ready to have a go at some questions on your own.

Let's have a go at this one.

So again, we're going to identify the digit in the third decimal place, which is the nine.

So we've got 0.

349, 0.

350.

Find our halfway point, identify where our number is going to be and then we can round up or down.

And in this case we're going to round up to 0.

350.

I'd like you please to have a go at this one.

Three decimal places again, 0.

8429, pause the video, good luck.

Come back when you're ready.

Let's take a look and see how you got on.

We identify the numbers to three decimal places either side, which is 0.

842 and 0.

843.

Identify the halfway point, decide which side your value is going to go.

And it's obvious here then to see that we are closer to 0.

843.

So that's what 0.

8429 is to three decimal places.

How did you get on? You got it right.

Absolutely super, well done, I knew you would.

Now you can have a go at these questions here.

So I've given you the number line there.

So you may have printed this out.

If not, you could just quickly sketch it out.

It doesn't need to be accurate.

And then I'd like you to work out your answer.

All of these are going to be to three decimal places.

Good luck, pause the video now and then come back when you're ready.

And the second half of this question.

Great work, let's take a look at those answers.

First one, 0.

007, then 0.

006, 0.

064 and 0.

065, and onto the second page, 0.

648, 0.

649, 6.

065, 6.

087.

Well done if you've got all of those right.

Now we are ready to move on to round to three decimal places.

Now you might say to yourself, hang on a minute, isn't that what we've just been doing? Yes it is, but we are going to look at how we do it without using that number line.

So if you don't want to draw the number line out, remember as always, it is absolutely fine to continue to draw out that number line.

Whatever you need to do to make sure that you get the right answer is fine by me.

We are going to round this to three decimal places and this time we're going to use our place value grid.

Here's our number and we're going to, just as we did before, we're going to identify the thousandths column because that is where the third decimal place is, which is here and we can see that the digit in that column is the eight.

We need to look to the right.

So we are considering now the number in the 10 thousandths column 'cause that's the immediately to the right of the thousandths column, which is a three.

What do we do when there's a three here? Do we round up or down? That's right, we round down because it's less than a five.

We're gonna round down to the lower value, and so we get 0.

67839, equal to three decimal places is 0.

678.

How about this one? Again, let's put it into our place value grid.

Let's identify the thousandth column because that's the third decimal place, and then we're going to consider the digit to the right, the one in the 10 thousandths column.

This time it's a seven.

Yes, you are right.

Of course, now we're gonna round up to the larger value.

I knew you'd be shouting that at me, superb.

Therefore we round the higher value, which is 1.

904.

You've really gotta hang this now, well done.

Let's take a look at this one.

Okay, here we go.

This time I'm gonna ask you to decide which digit I'm going to be identifying first.

That's right, good.

It's the eight 'cause it's in the thousandths column, which is the digit that's going to inform what I'm going to do next.

Well done, yeah, that's the three because that's in a column immediately to the right, in the 10 thousandths column.

It's less than five, so we're going to round down.

You can round to the lower value, and therefore it's going to be 0.

678.

And this one, let's pop it into our grid.

Let's identify and then let's look to the right.

So each of those steps are the same as we've been doing, which is why we've gone through them a little quicker.

But I knew you were ready for that.

Hmm, here, right, I've got a five.

So we know that that's exactly halfway.

So we know that in that situation we're always going to round up, we're gonna round the higher value, which is 0.

050.

Remember the need for that zero in that thousandths column.

Here we have Andeep and Sam and they have rounded 0.

0495 to three decimal places.

Andeep says, "My answer is 0.

05," and Sam says, "My answer is 0.

050." Whose answer is correct? Think about what we've just done on the previous slides.

Get your place value grid out if you need to or your number line.

Work out the answer and you'll be able to see then who you agree with, who is correct? Pause a video, when you've got your answer, pop back.

Who did you agree with? Now, even though we often consider 0.

05 and 0.

050 to be equivalent, if they're not the exact values, we cannot be sure.

Sam's value shows that they have considered the value in the 10 thousandths column, which means that Sam's answer is correct.

Now, I'd like you please to have a go at this question.

Which of the following round to 13.

470 when rounded to three decimal places? Pause the video, and then when you've got your answer come back.

How many of those did you decide would round to 13.

470? You should have B and C.

The top one is 13.

4693, which would round to 13.

469 to three decimal places and the bottom one would rank to 13.

471, not 13.

470.

You are now ready to have a go at this question.

If you don't have access to a printer, you could either copy out the grid.

If not, just have a go at working out the answers to the questions.

But if you can access the grid, then it's just like a word search.

You need to find the answers in the grid, pause the video.

Good luck, I hope you enjoy this task and then come back when you're ready.

Well done with that.

And now we're gonna move on to question number two.

We're going to use the clues to find the numbers being described.

Clue one, I am between three quarters and one.

Clue two, if you rang me to two decimal places, I round up.

Clue three, my tenths and thousands digits are the same.

Clue four, my hundredth digit is a quarter of my tenths.

Who or what am I, what is the number? Pause the video, look through each of the clues, and then decide what your answer is.

When you've got an answer, come back.

And another one of those.

And this time there are five clues.

Clue one, when rounded to one decimal place, I am 6.

8.

Clue two, when rounded to two decimal places, I round up.

Clue three, the sum of my digits is 29.

Clue four, my first digit is the same as my last digit.

And clue five, the digits in the tenths and hundreds columns are multiples of four.

I am what number? Again, pause the video.

Take as much time as you need to consider each of the clues and come back when you're ready.

And here we go with the final number detective question in this task.

This time, six clues.

Clue one, I am between three tenths and two fifths.

Clue two, when rounded to three decimal places, my thousandths digit stays the same.

Clue three, when rounded to two decimal places, I am 0.

32.

Clue four, the sum of my five digits is nine.

Clue five, I only have one odd digit.

Remember, zero is even.

And clue six, my largest digit is in the 10 thousandths column.

I am what number? Good luck with that one, pause the video.

I look forward to checking in with you when you get back.

Super work, well done, let's check in.

I hope you enjoyed these tasks.

So the first one, A, 0.

458, B, 1.

574, C, 3.

38, sorry, 3.

038, D, 6.

880, E, 2.

031, F, 27.

239, G, 0.

057, H, 4.

593, I, 5.

937, J, 3.

990, and remember that zero needs to be there because we are rounding to three decimal places, K, 3.

384, L, 0.

007, the James Bond one there, 007, M, 7.

350, and N, 3.

001.

Now if I've read through those too fast for you to keep up, remember you can pause the video and then you can come back to me when you are ready.

If you did have a go at the number search, that is where you should be able to find each of those numbers.

Let's move on to those number detective questions, that's what I'd like to call them 'cause there's clues.

The first one was 0.

828, the second one, part B was 6.

8456, and finally the final one was 0.

3204.

Now I really enjoyed making up those problems for you, so I really hope that you had fun trying to work out and solve the mystery of what those numbers were.

Now we are ready to summarise the learning that we've done in today's lesson.

This lesson we've specifically been looking at rounding to three decimal places and we can think of rounding to three decimal places as the same as rounding to the nearest thousandth.

A number line could be useful when rounding to three decimal places.

And there's an example there of when we looked at during this lesson.

Also a place value grid can be used when rounding to three decimal places.

And again, another example we looked at during this lesson.

Remember, it's absolutely okay to use either of those methods or you may have come up with a method of your own that works.

You've done really well in today's lesson and I've really enjoyed working alongside you and I look forward to seeing you soon, goodbye.