Lesson video

Hi there, my name's Ms. Lambell.

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 Degrees of Accuracy, and that's in the unit estimation and rounding.

By the end of this lesson, you'll be able to appreciate what is meant by a suitable degree of accuracy.

A degree of accuracy shows how precise a number or measurement is.

E.

g, we could say we have measured something to the nearest centimetre or to the nearest 10, or one significant figure.

These are just a few examples of degrees of accuracy and we'll explore these further in today's lesson.

Today's lesson, I've split into two separate learning cycles, in the first of which we will look at making sure we understand what we mean by a degree of accuracy, and in the second we will be able to apply that by answering questions to an appropriate degree of accuracy.

Let's get started on our first learning cycle.

Here we go.

Jun, Alex and Aisha are discussing the following statement.

Let's take a look and see what this statement they are discussing.

In 2022, the attendance at Glastonbury Music Festival was 210,000.

Jun says, "The first digit is in the 100,000s column." Let's just check, do we agree with Jun? Yes, he's right.

The first digit is in the 100,000s column.

"It must have been rounded to the nearest 100,000." That's Jun statement.

Let's have a look and see what Alex has got to say.

Alex says, "I don't think the attendance has been rounded." Alex is thinking that the exact attendance at the Glasbury Music Festival in that year was 210,000.

Aisha says, "The last non-zero digit is in the 10,000s column.

I think it has been round into the nearest 10,000." Let's just check the last non-zero digit.

Yeah, I agree with Aisha.

That is in the 10,000s column.

I'd like you to pause the video and have a think about who you agree with.

Pause it now and then when you come back, we'll take a look at this together.

Who did you decide that you agreed with? Let's take a look.

It was Aisha who was correct? Did you decide Aisha was correct? You did, brilliant, well done.

It could also have been rounded to the nearest 1,000, 100 or 10.

It could also be the exact value like Alex said, but it's extremely unlikely that there were exactly 210,000 people at the festival.

In 2022 the average cost of a house in the UK was 294,000 pounds.

What degree of accuracy is most likely to have been used here? What that's asking is, what do we think 294,000 pounds has been rounded to? The last non-zero digit is in the 1,000s column.

Therefore, it is most likely to have been rounded to the nearest 1,000.

So using the method that Aisha mentioned on the previous slide, we are looking and identifying in which column the last non-zero digit is, and here we can see that is the 1,000s.

That's why it's most likely to have been rounded to the nearest 1,000.

It could of course have been rounded to the nearest 100, nearest 10, or it could be the exact figure, but these are a lot less likely.

In 2022 the average number of people in each household in the UK was 2.

36.

Again, what degree of accuracy is most likely to have been used here? It's most likely that this has been rounded to the nearest two decimal places.

We can see there are two digits after the decimal point.

And let's take a look at this one.

In 2022 the average UK salary was 33,061 pounds.

Same question, what degree of accuracy is most likely to have been used here? It's most likely to have been rounded to the nearest integer.

That's the nearest pound in this case because we are talking about money.

We can see that the last non-zero digit is in the ones column, so the nearest integer.

And this one.

In 2023 the world record for the men's a 100 metre sprint is 9.

58 seconds.

Which degree of accuracy do you think has been most likely to have been used here? Here is most likely that has been rounded to two decimal places, so just over nine and a half seconds.

Two decimal places, we can see the two decimal places after the decimal point.

And that would be 100th of a second.

What about this one.

The average speed of a plane is 550 miles per hour.

Remember, that's what mph stands for, miles per hour.

Same question, what degree of accuracy is most likely to have been used here? Now here, I think we could reasonably say could be one of two things.

It most likely to have been rounded to the nearest 10, because if we look the last non-zero digit is in the 10s column, but also it ends in a 50, so it may have been rounded to the nearest 50.

Which of the following could be considered an appropriate degree of accuracy for the following? The size of a town is a 100,000.

Do you think it's been given to a, the nearest a 100,000, b, nearest 10 c, one significant figure, or d, the nearest 10,000.

Pause a video, have a think about this, and then come back and we'll check your answer when you've got one.

What did you decide? It could be a, nearest a 100,000.

We can see that the last non-zero digit is in the a 100,000s column.

It could also have been to one significant figure, because we've got one significant figure followed by placeholders of zeros.

It could also be rounded to the nearest 10,000.

It's not as likely to be the nearest 10,000, but it could have been rounded the nearest 10,000.

You are now ready to have a go at this first task.

You don't necessarily need to have this table drawn out exactly, you could just write down what you think the answers are for each of the following.

You are going to decide which is the most appropriate degree of accuracy for each of the following.

And you can choose from nearest integer, remember that's nearest whole number, nearest one, nearest 10, nearest 100 and nearest 1,000.

And the things I would like you to decide upon are the number of baked beans in a tin, the height at which a plane flies, the number of seats in five cinema screens, the number of people living in a street, the number of books in a page, number of buckets of water to fill a paddling pool and the number of grains of rice in one kilogramme.

Pose the video, decide which you think is the most appropriate degree of accuracy if we weren't going to write down the exact value, and come back when you've got your answers.

Pause the video now.

Superb, question number two.

Little bit more challenging here because I'm not asking you to tell me whether your rounded to nearest 10, 100, 1,000, I'm asking you to consider and use your knowledge of significant figures.

I'd like you to decide whether you think the most appropriate or most likely degree of accuracy for the following is one significant figure, two, three or four significant figures.

And the things I'd like you to consider please are, the population of a town is 12,000.

That means there are 12,000 people living in a town.

The length of a plank of wood is 6.

24 metres.

I have a plank of wood and I've measured it and it measures 6.

24 metres.

The next one, the width of a blade of grass is 1.

6 millimetres.

The attendance at a pop concert is 30,000.

Is of 30,000, we've rounded it.

30,000 people at the pop concert.

62% of UK homes own a pet.

And the next one, the width of a human hair is 0.

009 centimetres.

And finally, the distance from the earth to the moon is 384,400 kilometres.

Remember, you are deciding each of those figures and the context, and whether you think the most likely degree of accuracy was one, two, three or four significant figures.

Pause the video now, good luck with this.

Like I said, it's a bit more challenging than the first question, but I've got every faith that you'll be able to complete these correctly, good luck.

And question number three.

Don't be scared here, there's lots of information, okay, but we'll read through it together.

What I'm asking you to do is to rewrite the story, rounding each of the numbers to an appropriate degree of accuracy.

Like I said, I'm going to read through the story with you first and then as I read through it, I'm going to tell you what it is I would like you to change when you rewrite the story.

Sofia belongs to a supporters club for her favourite football team.

They decide to organise coaches to watch an away match.

19 coaches of 52 people set off the match.

The coach travels 262.

504 kilometres to the match which takes them three hours, 53 minutes and 15 seconds.

Whilst at the match, Sofia and her mum buy some lunch which costs 18.

97 pounds.

During the match there was an announcement that the attendance at the match is 51,699.

The average speed of the coach on the way home is 54.

89 miles per hour, and they arrive home at 23:58:42.

What I'd like you to do is to rewrite the story, but every time you see a number, I'd like you to round that number to an appropriate degree of accuracy.

Please pause the video now and when you've rewritten the story with all the different values in, come back and there will be ready to check your answers for task A.

Good luck with this, pause that video now.

How did you get on with that? We'll see, I'm sure you did fine.

Let's check our answers.

Question number one.

Number of baked beans in a tin be nearest to 10.

The height at which a plane flies would be nearest 1,000.

Number of seats in a cinema screen, nearest 100.

Number of people living in a street would be nearest 10.

Number of pages in a book, you may have chosen nearest 10 or nearest 100 depending on how big the book is.

Number of buckets of water to fiddler paddling pool, will be nearest integer.

And the number of grains of rice in a kilogramme, you may have chosen nearest 100 or nearest 1,000.

Either of those would be acceptable as an appropriate degree of accuracy.

Question number two, the population of a town is 12,000 has been given to two significant figures.

The plank of wood is 6.

24 metres is three significant figures.

The width of a blade of grass is 1.

6 millimetres, two significant figures.

The attendance a pop concept is 30,000 is one significant figure.

62% of UK home's owner pet would be two significant figures.

The width of a human hair is 0.

009 centimetres is one significant figure.

And finishing up with the distance from earth to the moon is 384,400 kilometres is correct to four significant figures.

Now let's take a look at the story.

Sofia belongs to a supporters club for her favourite football team.

They decide to organise coaches to watch an away match.

20 coaches of people, we would round the number of coaches to the nearest 10, so it would give us 20.

We've round the number of people on each coach to the nearest 10, that gives us 50.

50 people set off for the match.

The coach travels 260 kilometres.

We've given the distance to the nearest 10, to the match that takes them four hours, and here we've rounded that to the nearest hour.

You may have decided to round it to the nearest minute.

You also may have decided to round the 260 kilometres to the nearest integer, the nearest whole kilometre.

Whilst at the match, Sofia and her mum buy some lunch which costs 20 pounds.

We've given that to the nearest 10 pounds.

During the match there was an announcement that the attendance the match is 52,000.

Here we can see that the answer has been given to the nearest thousand.

The average speed of the coach on the way home is 55 miles per hour.

That's been given to the nearest in integer and they arrive home at 12:00 am, and that's been given to the nearest hour.

For that final one you may have decided to just leave off the number of seconds.

Some of your answers may be slightly different to these, but I'm sure you understand now this idea of an appropriate degree of accuracy.

Now we can have a look at the final learning cycle for today's lesson where we are going to look at actually answering some questions and making sure that the answers we give are given to an appropriate degree of accuracy.

Calculate the area and perimeter of the shape.

Give your answer to an appropriate degree of accuracy.

We can see the dimensions of our shape are 8.

4 centimetres and 3.

7 centimetres.

Looks to me like Aisha and Jun are going to have a little conversation here.

Let's see, let's listen into their conversation.

Aisha says, "What does it mean by an appropriate degree of accuracy?" So often we will be told in the question, we need to give our answer to the nearest whole number or to the one decimal place or to two decimal places.

But here the question is asking for our answer to an appropriate degree of accuracy.

And Aisha at the moment she will be saying, at the moment she's not quite sure as to what that means.

Jun says, "If it was money, it would be two decimal places, that would be appropriate." That's right, isn't it? 'Cause if we are doing money, we can count up in pennies which is to two decimal places.

Aisha says, "Yes, that's right and if not, give it to the same degree of accuracy as the values in the question." So she just needed that little prompt and now Aisha has remembered that if we are not told the exact degree of accuracy, then we use the same as the accuracy of the values in the question.

And here we can see Jun says, "That each of the dimensions has been given to one decimal place.

So we'll give our answers to one decimal place.

The area, remember to calculate the area of a rectangle, we do the length multiplied by the width, we're going to do 8.

4 multiplied by 3.

7 which is 31.

08.

But remember each of the values in the question are to one decimal place.

So our appropriate degree of accuracy for our answer would be one decimal place, and I know you know how to round 31.

08 to one decimal place.

It's 31.

1.

Remember we're talking about an area, so it's square centimetre, centimetre squared.

The perimeter, so here I've decided to add together my two sides and double it.

You may just decide you're gonna do 8.

4 add 3.

7, add 8.

4 add 3.

7.

There are lots of ways to calculate the perimeter.

So here I work out my brackets first because of my priority of operations and I do brackets first.

That gives me two multiplied by 12.

1.

So my answer is 24.

2.

My answer here is already to one decimal place.

Let's have a look at an exchange rate problem.

The exchange rate of pounds to euros is one pound to 1.

16 euros.

We're going to convert the price of the ice cream into pounds, and we're going to give our answer to an appropriate degree of accuracy.

I'm going to draw a ratio table and here it is.

With my conversion at the top, one pound is equal to 1.

16 euros.

We know the cost of the ice cream in euros.

Euros is on the right hand side of my ratio table, so I'm going to put the 2.

20 on the right hand side at the ratio table underneath euros.

I'm now looking for a multiplicative relationship and I've decided to move from pounds to euros because that's much easier than going from 1.

16 to 2.

2.

Moving from pounds to euros, I'm multiplied by 1.

16.

What happens when I move back from euros to pounds? I'm going backwards, therefore I'm going to do the inverse operation.

I'm going to divide by 1.

16.

2.

2 divided by 1.

16, here it is on my calculator.

What would be our appropriate degree of accuracy in this question? Yeah, that's right, it's gonna be two decimal places because we're talking about money.

We'd give it to the nearest penny and here we can see that 1.

8965, et cetera would round to one pound 1.

90.

Since we are talking about the amount of money, like I said, the appropriate degree of accuracy is going to be two decimal places.

The equivalent cost of the ice cream in pounds is 1.

90.

Andeep is helping his uncle work out how many boxes of grass seed are needed to cover this piece of garden.

So we can see here the dimensions and the shapes for an L shape piece of garden, and Andeep's uncle wants to put some grass seed on it.

One box of grass seed covers approximately 10 metres squared and it costs seven pounds.

How many boxes do they need? Let's take a look at this one together.

Firstly, we need to calculate the area of the garden.

Here's my garden.

I've just made it a little bit bigger so it's easier for us to see.

First, we need to find any missing dimensions.

We can see that the base is 2.

4 add 2.

4 'cause we can see the two horizontal values at the top of our shape are 2.

4 and 2.

4.

So the base of my shape, of my L shape is 4.

8 metres.

Now we need to work out what those two missing vertical lengths are.

We can see that the entire height of the L shape is 4.

8, what do those two dashes on those sides mean? Yeah, it means they're equal in length.

So I need to take my 4.

8 and divide it equally into two parts.

So divide by two.

This gives me that each of those is 2.

4 metres.

There are various ways you can go about finding the area of this shape.

I've decided to complete the square, so I'm adding in the extra sides to make the square and then gonna calculate the area of as if it was an entire square and I'm going to subtract the area of the white square.

Giving me the calculation 4.

8 multiplied by 4.

8, that would be if it was the entire square, but I'm taking away that white bit because that's actually not part of my garden.

So I'm subtracting 2.

4 multiplied by 2.

4.

The area of the shape is 17.

28 metres squared.

Although this is to a greater degree of accuracy than the values in the question, we would not round at this point.

Rounding should only take place when giving the final answer.

So we're going to leave that at 17.

28 for the moment.

One box of grass seed covers approximately 10 metres squared and costs seven pounds.

How many boxes do we need? That's the next part of the question that we need to consider.

Area of the garden we've just calculated is 17.

28 metres squared.

The number of boxes, we need to take the total area and divide it by the area that one box covers, which in this case is 10.

That gives us an answer of 1.

728 which is two.

I can't buy 0.

728 of a box.

So here I need to round up and I need to buy two.

Now I can calculate my cost.

I know that I'm buying two boxes at cost of seven pounds each.

That means it's going to cost me 14 pounds, or not me, Andeep's uncle, cost him 14 pounds to put grass seed on that piece of his garden.

Sometimes there may be no context to our question at all like this one.

These questions we will use our calculator for.

It says calculate the following giving your answer to an appropriate degree of accuracy.

Firstly, we will decide on our appropriate degree of accuracy.

What do you think it might be? What do you think an appropriate degree of accuracy is here? They do not have the same number of decimal places.

If we look 17.

2, that's got one decimal place, 5.

68, it's got two decimal places and 254 has no decimal places, but they do each have three significant figures.

We can see each of them consists of three figures.

Therefore we're going to give our answer to three significant figures.

We're going to put this into the calculator.

So this is the calculator that I'm using, remember yours might be slightly different.

Here I've given you on the right hand side the buttons that I have pressed.

So that if you've got this calculator, then you will know which button to press.

If you haven't, then you should already by now hopefully know how to use the fraction button on your calculator to enter in this calculation.

I'm then going to change that into a decimal and we are giving this to three significant figures.

So three significant figures.

I'm going to count my significant figures, will be the four would be the first, then the five be the second, and then the three would be the third.

I look at the digit after that which is a five, so I round up.

It'll be 0.

0453 to three significant figures.

Notice here I've not written down the entire calculated display, I've written and I've shown that this number continues with the use of an ellipsis.

Have a go now at this check for understanding.

I'd like you to match each problem on the left hand side to what you think the most appropriate degree of accuracy would be for your answer.

Pause the video and then when you are ready, come back and we'll check those answers.

Let's see how you got on.

Converting dollars into pounds, that's where we need two decimal places.

The area of a square with sides 5.

6 centimetres, that's going to be one decimal place.

The number of boxes needed for 95 eggs is going to be one significant figure.

I need a whole number of boxes, I can't have a decimal number of boxes.

So the final one by default is two significant figures, but if we look at each of our numbers, we can see that they've each got two non-zero digits, so two significant figures.

Now you are ready to have a go at task B.

Stick with me, we're nearly there at the end of this lesson.

Well done so far and we've just got a little bit extra to do.

In each of the following questions, you're going to give your answer to an appropriate degree of accuracy.

I'd like you to calculate the area and perimeter of those two shapes.

Remember to give your answer to an appropriate degree of accuracy.

You may use your calculator, but as always make sure you write down the calculations so that if you've made an error, you can see exactly where you've gone wrong.

Pause the video now and I'll be waiting here when you get back.

Great work on those.

Now let's move on to question number two.

In each of the following questions, you are again going to give your answers to an appropriate degree of accuracy.

I'd like you to convert the following from dollars into pounds, using the exchange rate that one pound is equal to $1.

27.

Again, here you will need to use your calculator.

That's absolutely fine, but make sure you make a note of your calculations.

Pause the video and good luck with these.

Super, and then finally question number three.

Again, at each stage you're going to give your answer to an appropriate degree of accuracy.

How much will it cost to paint this wall? If one tin of paint covers 25 metres squared, and each tin of paint costs 19.

50 pounds, good luck with this one.

Little bit more challenging, but you've definitely got all of the skills you need to get the right answer to this.

So stick with it, work hard, and I know you'll come back with the correct answer.

Good luck, pause the video now.

Great work now we are ready to do the last two questions of this lesson.

And these are calculated questions, so using your scientific calculator, given your answers to an appropriate degree of accuracy, answer the following.

Pause a video, and then when you get back, I think we'll be done and ready to mark our answers and then finish up with a summary of our learning for today.

You've done really well so far.

Just stick with it for a little longer and then we'll be done, good luck.

And here we are at the answers.

One a, the perimeter was 13.

8 centimetres and the area was 8.

3 centimetres squared.

And that was to one decimal place because each of the values in the question were to one decimal place.

b, the perimeter was 9.

86 metres and the area was 4.

67 metres squared to two decimal places because that's the degree of accuracy used in the question.

Question two, both of these should have been given to two decimal places because it was talking about currency, about money.

a, was 2.

32 pounds and b was 4.

49 pounds.

Question three, the area of the wall was 40.

47 metres squared.

The number of tins of paint is three and the cost of the paint is 58.

50 pounds.

And there you can see all of the steps of working out that you can check each of your steps if you need to.

And finally, question number four.

If we look at the values in four a, each of them had two significant figures.

So my answer is 0.

022 to two significant figures, and then if we look at b, we can see that each of them has two decimal places, which is why my answer I've given to two decimal places, which is 449.

64.

Now we can summarise the learning from today's lesson.

Degrees of accuracy show how precise a number or a measurement is.

If the degree of accuracy is not stated, you can make a conjecture about what you think it might be.

So if we think about those first questions we looked at when we looked at the price of the average house in the UK, we predicted we made a conjecture.

It's a conjecture because it's not yet been proved that that value had been given to the nearest 1,000.

When we're working with money, we must make sure that our answers are given to two decimal places.

And if a question does not ask us or give us the required degree of accuracy in the question, then our answers should be given to the same degree of accuracy that the values were given to us in the question.

Great work on that.

Some quite tricky things to get your head around today, so well done for sticking with me all the way till the end.

Done fantastically well like you said, and I really, really hope to see you again very soon to do some more maths.

Thank you, goodbye.