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I can round numbers to any number of decimal places.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Numbers with any number of decimal places can be represented on a number line.
Any number can be rounded to a given number of decimal places.
It is possible to identify the most suitable number of decimal places from the context.
It can be useful to think about what the biggest and smallest values of a number rounded in context were.

Common misconception

Pupils think that repeated rounding gives the correct answer.

Use a number line to support pupils’ understanding. Locate the number to be rounded on the line and identify the critical values.

Keywords

Round - To change a number into another number that is approximately the same value but is easier to work with. E.g. round 561 to the nearest 10 is 560.

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Hi there.

My name's Ms. Lambdowe.

You've made such a super fantastic choice, decided 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 Any Number of Given Decimal Places.

By the end of this lesson, that's exactly what you'll be able to do.

You'll be able to round numbers to any number of decimal places.

A keyword that we'll be using in today's lesson is round.

You're super familiar with this by now, but just a quick reminder, when we round, we change a number into another number that is approximately the same value that is easier to work with, and our example here is that 561 rounded to the nearest 10 is 560.

Today's lesson is split into two learning cycles.

In the first one we'll look at rounding to any number of given decimal places.

Now you're already really good at this because we've done 1, 2, and 3 decimal places.

What we'll do today is just make sure that we are really confident with switching between them, and in the second learning cycle we will look at rounding in a context.

Here we go with that first learning cycle.

Let's get going.

We're going to round 0.

67839 to 1 decimal place.

I'm going to jump straight into using the place value grid.

If you need to remember, you can actually draw out your number line if you find that more useful.

But we've done lots of practise on that recently so I'm pretty certain that most of you will be able to go straight in with the place value grid.

I'm going to place my number into the grid.

We are rounding to 1 decimal place.

What column is the first decimal place? It's the tenths column.

So we identify the tenths column and we can see that's here.

We can see the digit in our tenths column is 6.

We need to consider the digit in the hundredths column because that's the column that is immediately to the right.

Here, that is a 7.

7 is greater than 5, therefore we increase the tenths digit by 1, making this 0.

7 to 1 decimal place.

And now the next one.

Round 45.

8749 to 2 decimal places.

Let's put that into our place value grid, remembering to line up the decimal point.

45.

8749.

Identify this time the hundredths column as that is the second decimal place.

Here's the hundredths column and we can see that our digit here is 7.

We need to look at the thousandths column 'cause this is the column immediately to the right.

This will inform us as what we are going to do with that 7.

Is it gonna stay as a 7 or we are going to increase it by one hundredth? Here we can see that 4 is less than 5.

Number 5 is that critical value where we decide we are going to start rounding up.

Therefore we keep the hundreds digit the same.

45.

8749 is equal to 45.

87 to 2 decimal places.

And this one, round 25.

3065 to 3 decimal places.

Let's put it into our place value grid.

Remember to line up our decimal points so everything is in the right column.

We're gonna identify this time the thousandth column is the third decimal place, a thousandth column and our digit in this column is a 6.

Remember then we are considering the column that immediately to the right, which in this case is the ten thousandths column.

This is a 5, it's exactly halfway.

Remember, when it's exactly halfway, we always round up to the larger value, so we are going to increase the thousandths digit by 1.

We're gonna increase that thousands digit by 1, giving us 25.

307 to 3 decimal places.

Aisha and Jacob are rounding 0.

3098 to 3 decimal places.

Aisha says it's 0.

310.

Jacob says it is 0.

3010.

Who is correct? Let's take a look.

3098.

We are rounding to 3 decimal places so we need to identify the digit in the thousands column which is the 9.

We look to the ten thousandths column and we look at the digit there, which is an 8.

This is greater than 5, therefore we need to increase the hundredths digit by 1.

Aisha is correct.

If we add 1 thousandth to 0.

309, we get 0.

310.

Jacob has increased 9 to 10 and he has not exchanged the 10 thousandth for 1 hundredth.

That's a really common mistake.

We have to be really careful, particularly if it's a 9 you are going to be changing, so just warning you, make sure you keep an eye out for those ones.

You are ready now to have a go at task A.

Here I've given you a table.

You've got the number on the left hand side.

You are going to round that number to 1 decimal place, 2 decimal places and 3 decimal places.

It's really important here that you go back to the number in the first column when answering these questions.

You can pause the video now and I'll be here when you get back.

Great work.

Question number 2.

We're now going to be looking at what I like to call number detective problems. I'm going to give you some you some clues and then you are going to need to try and work out what number is being described in each of these.

The first one, part A, has 5 clues.

Clue 1, I am between 2 and 3.

Clue 2, I have 3 digits after the decimal point.

Clue 3, when rounded to 2 decimal places I am 2.

88.

Clue 4, my hundredths digit is greater than my thousandths digit.

And clue 5, the difference between my tenths and thousandths digit is 2.

You may want to have a place value grid handy for this question.

You can pause the video now, work out what my number is and then when you're ready come back and I'll share the next question with you.

Good luck.

Well done.

Hopefully you've come to a number.

There should just be one answer.

Let's now move on to part B of question 2.

The clues this time are, clue 1, I'm between 1 and 2.

Clue 2, I have 3 digits after the decimal point.

Clue 3, when rounded to 1 decimal place I am 1.

Clue 4, when rounded to 2 decimal places, I am 1.

90.

And clue 5, the sum of my tenths and thousandths column is 13, what number am I? Pause the video, and come back when you've got your answer.

Great work.

And part c, clue 1, I am between 0 and 1.

Clue 2, I have 3 digits after the decimal point.

Clue 3, when rounded to 1 decimal place I am 0.

Clue 4, when rounded to 2 decimal places I am 0.

08.

And clue 5, my hundredths column is double my thousandths column, I am what number? Pause the video.

Come back when you can tell me what number I am.

Great work.

Let's check in those answers then.

So number 1, I'm going to go across the top.

So the first one, 14.

3, 14.

25, 14.

253.

Row two, 765.

3, 765.

32, 765.

325, row three, 2035.

8, 2035.

84 2035.

837, row four, 7.

7, 7.

66, 7.

658, row five, 82.

8 82.

83 82.

829.

I've lost count now I think it's row six, 0.

6, 0.

63, 0.

635, row seven, 0.

1, 0.

09, 0.

087.

And the final row, row eight, 0.

3, 0.

30, I hope you've remembered to put that zero there, and then the final one, 0.

300.

Again we need those three zeros to show we've rounded to 3 decimal places.

Now if I did those two quick obviously pause the video, check them, and then when you come back we'll move on to looking at the answers to those three number detective problems. And here we go.

A, the correct answer was 2.

876.

B, it was 1.

904, and C, 0.

084.

How did you get on with those? You managed to detect all of those numbers, that's fantastic, well done, I knew we would.

Let's now then move on to our final learning cycle of this lesson, and we're going to be looking at rounding in context.

In 2022, at the FINA World Championships, 25 metres, the headlining event was the last race.

It was the men's 4 x 100 metres.

This is the swimming championships here.

The result of the race was a dead heat, meaning that the USA and Australia both got the gold medal and a new world record.

So this was a swimming race.

The pool was 25 metres long and it was a 4 x 100 metres.

So that means that each person, each swam four lengths in the four different strokes.

Now it says that they both got the gold medal and a new world record.

The new world record was 3 minutes 18.

98 seconds.

Alex is saying do you think it was actually a dead heat? A dead heat means both teams got exactly the same time.

Aisha says, I think that if they could measure the time to a greater degree of accuracy, it probably would not have been.

And Alex says, I think you're right Aisha.

Maybe if the time had been measured to the nearest thousandth of a second there would be a difference.

Sometimes, limitations of measuring can have an effect on outcomes.

So I think that actually Alex is right.

If they were able to measure the time to the nearest thousandth, then probably there would've been a difference between the two.

But given that the times were only measured to the nearest hundredth of a second, they both got the same time.

It's worth remembering sometimes our limitations of measuring will affect our outcomes.

Lucas is working on a project.

He has 3 metres of material and cuts it into 30 centimetre pieces.

So we are going to have a look now at what effect measurement may have on what Lucas ends up with.

How many pieces can he make? His piece of material is 3 metres long.

You'll need to convert that into centimetres, you know how to do that.

And then he's going to cut this piece of material into pieces that are 30 centimetres in length.

How many pieces can he make? 3 metres is 300 centimetres.

Remember, there are 100 centimetres in a metre, so that's 300 centimetres divided into 30 centimetre pieces.

This means that Lucas would be able to make 10 pieces.

But Lucas says he's measured his last piece.

He's cut them all up and his last piece is less than 30 centimetres.

Why might Lucas's last piece be smaller than the rest? Measuring, there are frequently errors.

Even very small errors can become much larger if repeated.

Lucas has recognised that his ruler only allows him to measure to the nearest millimetre, we are now gonna have a look at what effect this could have on Lucas's pieces of material.

Lucas cuts each of the first 9 pieces 1 millimetre longer.

What would be the length of the final piece? So each piece is going to be 1 millimetre longer.

What would be the length of the final piece? Let's take a look.

We know the length of the piece material is 300 centimetres.

He's going to cut the first nine, because the 10th piece is just going to be what's left basically, and he's going to measure those 1 millimetre longer than the 30 centimetres.

This is my calculation, and we can see that actually his final piece is going to be only 29.

1 centimetres in length rather than 30.

So we can see that this very small error of 1 millimetre, I think you'll agree that 1 millimetre is a very small error but it has a much bigger impact on the size of the last piece because we've repeated that error over the 9 first pieces of material he cuts Lucas now says, what happens when I cut each of the first 9 pieces 1 millimetre shorter than I should have, so if he wasn't quite accurate with his measuring.

This time he's cutting them 1 millimetre shorter.

So he's going to cut 9 pieces at 29.

9, and this time we can see that the piece that he's got left over is actually 30.

9 centimetres.

Again, we can see that this very small error of 1 millimetre has a bigger impact on the size of the last piece of material.

Let's now take a look at this problem.

This area needs to be carpeted.

We can see the dimensions of the area to be carpeted and we can also see the cost per metres squared.

It costs £5.

29 per metres squared.

We're going to take a look at Aisha, Lucas and Jacob's workings, and we're going to think about whether they've answered the question correctly or not.

Here's Aisha's working.

Aisha's done 3 x 1 = 3 metres squared, and then 3 x 5.

29 is £15.

87.

Why has Aisha rounded the dimensions of the room? Have a think about that for me.

The carpet is sold in square metres.

We can see that, £5.

29 per metres squared, so it's sold in square metres.

So Aisha has decided to round each of the dimensions to the nearest metre.

How do we know that this area of carpet will not cover the whole room? Aisha has rounded both of the measurements and both of them gotten smaller, so she's going to end up with a piece of carpet that isn't quite big enough for the room.

Here's Lucas's workings.

He's done 3.

24 x 1.

26.

I think that's the correct way of working out.

In fact, I know that's the correct way of working out the area of that rectangle, giving an answer of 4.

0824 metres squared.

He's then done 4.

0824 x 5.

29.

So the area that needs to be covered multiplied by the cost per metres squared, and gives an answer of 21.

595896.

Why is Lucas's method not appropriate? Giving the area of the floor to 4 decimal places is not appropriate.

Carpet would not be measured to this degree of accuracy.

What about the cost? Why is the cost not appropriate? Cost is not appropriate because it would need to be rounded to 2 decimal places.

When we are working with currency, we need to make sure we've rounded to 2 decimal places.

Let's take a look at Jacob's workings.

Jacob, he's got the same calculation as Lucas did for the first part, but he's got a slightly different answer of 4.

08 metres squared.

He's then taken the 4.

08 and multiplied by the cost per metre, giving the total cost to carpet that area as £21.

58.

Jacob's method is the most appropriate.

He has given the area correct to 2 decimal places and he has given the cost to 2 decimal places.

Generally, answers are given to the same degree of accuracy as the values in the question, unless otherwise specified in the question, here, we were not told what degree of accuracy to give our answer to.

So we look at the values in the question and we can see that all of the values have been given to 2 decimal places.

Therefore I'm going to give my answers to 2 decimal places.

Which option shows the appropriate calculations to calculate the cost to carpet the room? The dimensions of the room have changed and the cost per metre squared carpet has changed.

You're going to pause the video, decide whether you think it is A, B or C that is the correct appropriate calculations for calculating the cost of carpeting this room.

Pause the video now and then when you get back we'll go through the answer.

What did you decide? I hope you didn't guess.

No, of course you didn't.

The correct answer was B.

We can see that the first one has done the area of the carpet and so has the second one.

C, remember is incorrect.

We would actually end up with too much carpet in one direction and not enough carpet in the other direction.

We can see that A has rounded to 3 decimal places, but actually here, we would want to round 2 decimal places.

And also, A, we can see that the cost has been given to 3 decimal places and we know that a cost must be given to 2 decimal places.

That's why B is the correct answer.

You're now ready to have a go at these questions here.

So, 3 friends go out for lunch and spend £25.

They decide that there are 3 different ways that they can pay.

I'd like you, part A, to write down the pros and cons of the different ways, and the different ways are, they round the cost to the nearest £10 and split the bill.

Two, split the bill between the 3 of them and round this to the nearest pound and each pay that amount.

And three, split the bill between the 3 of them, round to 2 decimal places and each pay that amount.

Part B, I'd like you to decide what should they have done to pay for their lunch.

You can pause the video now and I'll be here when you get back.

You may use a calculator to work out the answers to these questions.

Good luck with these.

And question number 2.

So we are looking at the carpeting questions now.

I'd like you please to work out the cost of carpeting those two areas.

Part B is a little more challenging, but you have looked at shapes like this previously.

Good luck and I'll see you when you come back.

You can pause the video now.

Great work.

And then we'll move on to question number 3.

Lucas, Aisha and Jacob take part in the 800 metres on sports day.

The teacher recorded their times to the nearest minute.

Here are their times.

Lucas, 3 minutes, Aisha, 3 minutes, Jacob 3 minutes.

Part A, I'd like you please to answer the question, was rounding to the nearest minute a suitable degree of accuracy? B, the teacher then decides to record their times to the nearest hundredth of a second.

Is this an appropriate degree of accuracy? Pause the video, have a go at these and then come back when you're ready.

And the final question for today's lesson is, here are their exact times.

Was it necessary to record the times to the nearest hundredth of a second? Pause video, and then when you come back we'll check all of those answers and then we'll be almost done for today's lesson.

Stick with me just for a little bit longer.

You've done fantastically well so far.

And here we go with the answers.

1a, round the cost to the nearest £10.

So 25 rounded to the nearest 10 is 30.

We split that between the three people giving us £10.

They each paid £10.

So a pro is that they cover the cost of the lunch, but a con may be that they paid £5 more than they needed to.

Let's look at scenario two where they split the bill between the three of them and rounded to the nearest pound and each paid that amount.

So the cost of the lunch was 25 divided by the 3 friends, that gave us £8 to the nearest pound, but 8 x 3 is 24.

So a pro may be that it is easy to work out, but a con would be that they are pound short for the cost of the lunch.

They don't have enough money to pay for the entire lunch.

And the third scenario, this is where they were going to split the bill between the 3 of them and round to 2 decimal places, and each play that amount.

We start with the same calculation as we did in the previous one, but this time we are giving our answer to a greater degree of accuracy.

So rather than giving our answer to the nearest integer, to the nearest pound, we are giving it to 2 decimal places, which gives us £8.

33.

Now we need to check, if each 3 people pay £8.

33 each, they have paid £24.

99.

Pro would be that they pay the same amount each, but a con would be that they are 1p short on the cost of the lunch.

What should they have done? They should have divided the cost by 3, but round up to the nearest penny to make sure that they've got enough to cover the cost.

Question 2 part a.

The area of the carpet was 49.

0 metres squared, meaning the cost to cover that area is £306.

25.

Part b.

The area was 29.

88 metres squared, giving us a total cost to carpet that area of £177.

79.

Question 3 part a, was rounding to the nearest minute a suitable degree of accuracy? No, because the times were all the same.

The teacher then decides to record their times to the nearest hundredth of a second.

Is this an appropriate degree of accuracy? Yes, this should definitely separate the pupils.

Here are their exact times.

Was it necessary to record the times to the nearest 100th of a second? It was not necessary, as we could tell from the tenths of a second.

Now we're ready to summarise the learning from today's lesson.

A place value table is useful when rounding to decimal places, take care when the digit in the column that needs altering is a 9.

And there's an example there of the mistake that Jacob made and the mistake that I know you won't make.

Limitations of measuring can have an effect on outcomes.

Generally, answers are given to the same degree of accuracy as the values in the question, unless otherwise specified in the question.

So that was like our examples that we did with the carpet.

You've worked fantastically well today.

I've been really, really impressed with what you've done.

Thank you for joining me and I really look forward to seeing you again.

Bye.

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three decimal places." }, "questionType": "Short answer", "correct": [ { "text": "0.057" } ], "id": "893c8dad-441d-a8c1-fd27-2d9c6cef0d44", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" }, { "type": "Question", "question": { "text": "Round 203.0995 to three decimal places." }, "questionType": "Short answer", "correct": [ { "text": "203.100" } ], "id": "67787b15-1cdf-eb12-bb2f-ddfcc914077e", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" } ], "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9", "meta": { "gradeStageId": "ks3", "subject": "Maths", "grade": "Year 8", "topic": null, "unit": "Estimation and rounding", "lessonCount": "16", "age": [ 12, 13 ], "gradeId": "age_12_13", "gradeStage": "Key Stage 3", "lesson": "Rounding to any number of decimal places" } }, { "id": "98222434-15d6-60d7-6590-f0517a527c2b", "type": "Resource", "resourceType": "Quiz", "title": "Rounding to any number of decimal places", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "If a degree of accuracy is not stated in a question that you are answering, you should use the ______ degree of accuracy as the values in the question." }, "questionType": "Short answer", "correct": [ { "text": "same" }, { "text": "identical" } ], "id": "14afec37-3834-acd2-fa22-04d4e92707bc", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" }, { "type": "Question", "question": { "text": "Round 5.072 to two decimal places." }, "questionType": "Short answer", "correct": [ { "text": "5.07" } ], "id": "4caffe8c-2314-2e7b-4a5b-6f722de87533", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" }, { "type": "Question", "question": { "text": "Round 34.072 to one decimal place." }, "questionType": "Short answer", "correct": [ { "text": "34.1" } ], "id": "2194a32c-8f4d-bb9f-a37b-dc951c36e1f1", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" }, { "type": "Question", "question": { "text": "Round 135.98 to one decimal place." }, "questionType": "Short answer", "correct": [ { "text": "136.0" } ], "id": "11c3d955-3161-db19-06c9-c588ec65b59d", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" }, { "type": "Question", "question": { "text": "Calculate the cost of carpeting this area.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1706259846%2Fkjfquvuima5ezls5eo18.png&w=750&q=75", "imageKey": "98222434-15d6-60d7-6590-f0517a527c2b/question/6359dd38f21c08703823e9da8e16630a.png" }, "questionType": "Short answer", "correct": [ { "text": "£69.72" }, { "text": "69.72" } ], "id": "5def95b1-0e5b-cd3c-7251-bf0065246f66", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" }, { "type": "Question", "question": { "text": "3 friends go out for lunch and spend £28. They pay the same amount each. What is the smallest amount they each pay to cover the cost of the bill?" }, "questionType": "Short answer", "correct": [ { "text": "£9.34" }, { "text": "9.34" } ], "id": "284dff79-fc27-a5c3-68ac-c520f80ada9a", "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9" } ], "lessonId": "b895290f-a0cc-bbf6-3e9f-cf4fe6ab3ea9", "meta": { "gradeStageId": "ks3", "subject": "Maths", "grade": "Year 8", "topic": null, "unit": "Estimation and rounding", "lessonCount": "16", "age": [ 12, 13 ], "gradeId": "age_12_13", "gradeStage": "Key Stage 3", "lesson": "Rounding to any number of decimal places" } } ] }