Lesson video

Hi there.

My name's Miss 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 Integers to Significant Figures, and that's in the unit Estimation and Rounding.

By the end of today's lesson, you'll be able to round integers to a required number of significant figures.

You are already familiar with the term significant figure and you've already probably looked at rounding to one significant figure.

Let's just quickly remind ourself of some keywords that we are going to be using in today's lesson, and those are significant figures and round.

Significant figures are the digits in a number that contribute to the accuracy of the number.

The first significant figure is the first non-zero digit.

Really important to remember the first non-zero digit.

Round; this is when we change the number into another number that is approximately the same value but is easier to work with, and you'll look at that later on in this unit; how we are going to use these rounded values.

Today's lesson is split into two learning cycles.

In the first one we're going to look at using a number line for significant figures and in the second one we'll look at alternative methods of being able to round to a given number of significant figures.

Let's get going on the first one.

Here we have Andeep and Laura.

Andeep and Laura know how to round to one significant figure.

Like I said in the introduction, I'm sure you do too.

They are now looking at how they might round to more than one significant figure.

They're going to round 34,702 to two significant figures.

They know that it would be 30,000 to one significant figure, but they want to move their learning on.

Good for them.

Andeep says, "I think that the second significant figure is 4 as the first one is the 3." Laura says, "I agree, Andeep, and the second significant figure is in the thousands column." "That means we are going to round to the nearest thousand then? That's a question that Andeep is posing, and Laura says, "Yes, that's right." We look at the column that the second significant figure is in.

In this case it's the thousands, so we round to the nearest thousand, and I know you are really, really good at rounding into the nearest 10 hundred thousand, and beyond that.

Andeep says, "I would like to practise identifying the correct digit in a number for different significant figures." Laura says, "Try these, Andeep." The third significant figure of 5,678 is.

"I think it's the 7." "Yes, that is right.

Well done." The second significant figure of 12,345 is.

"I think it is the 2." "Well done, Andeep." The first significant figure of 67 is.

"I think it's the 6." "Right again." The third significant figure of 203,568 is.

Andeep says, "I'm not so sure on this one.

Does the zero count as significant?" And Laura's response is, "Yes, it does, Andeep.

Any digit after the first significant figure is significant." I can see here why Andeep paused because he knows that the first significant figure is the first non-zero digit and so he's worried about those zeros, but like Laura says, once we start counting, the 2 is the first significant figure, then the zero would be the second significant figure and the 3 would be the third significant figure.

And that's what Andeep has noticed.

"Andeep," Laura says, "you are definitely ready to start rounding to any number of significant figures." What is 547 to two significant figures? Here's our place value grid.

The first significant figure, remember the first non-zero digit and 5 is not zero.

This is our second significant figure.

It is in the tens column.

The second significant figure is in the tens column.

It just means then, that we are going to rank this to the nearest 10.

We know how to do that on our number line.

We identify the multiples of 10 that are below and above 547, which are 540 and 550.

What do we do then? Yep, you're right.

We find the midpoint, which is 545.

We then need to decide where 547 is on our number line and we know that that's bigger than 545.

Remember, it doesn't need to be accurate.

We just need to know if it's going to be to the left or to the right.

547 rounded to two significant figures is 550.

Notice this is no harder than rounding to the nearest 10.

It's just this new terminology of significant figures.

All of these numbers below have nine zeros.

How many zeros does each number actually need to preserve the place value of the other digits? I'm gonna give you a moment, pause the video and come back when you've decided which of those zeros are actually needed.

What did you decide? Let's see.

Let's check those answers.

Here, these zeros are not needed.

Only one of them is.

The trailing zeros after the decimal point are not needed.

Let's look at the next one.

These two are not needed.

They are trailing zeros after the decimal point, but we need the other seven zeros.

This one, we actually need all nine of the zeroes because we don't have any trailing zeroes at the end.

In this one, these are our trailing zeroes which are not needed and so therefore I need six of the zeroes.

Here, again, trailing zeroes not needed, so I need four of them.

And the final one, I actually need all nine zeroes.

So it's really important to recognise when zeroes are significant and when they are not.

Which of the following have zeros which are not needed to preserve the place value of the other digits? You can pause the video and then when you've got your answer, come back and we'll check it.

What did you decide? B And C.

We can see that these two have trailing zeros after the decimal point.

Trailing zeros just means extra zeros after the decimal point at the end of the number, and that's important.

It's not just zeroes after the decimal point, it's redundant ones that are at the end of our decimal.

What is 23,924 to three significant figures? Let's put it in our place value grid.

Our first significant figure 'cause it's not zero.

Now we're gonna continue to count.

Second significant figure and third significant figure.

What column is it in? It's in the hundreds column.

The third significant figure is in the hundreds column, therefore we round to the nearest hundred.

Let's put this on our number line.

Our multiple of a hundred below 23,924, which is 23,900.

And what's our multiple of a hundred that is above 23,924? That's 24,000.

Let's find our halfway point.

Remember from previous learning that if you're not sure what the halfway point is, you can sum the two values on your number line and then find half of that.

Let's place our number on the number line and we can see that it's to the left, therefore it is going to round to 23,900 to three significant figures.

Now let's take a look at this one.

Into our place value grid.

Which is the first significant figure? That's right, it's the 6.

That's the first digit that isn't zero.

What about the zero in the thousandths column? Is that significant? Yeah, you're right, it is because we've started counting.

Second significant figure and third significant figure.

Once we've started, we need to continue, even if they are zeros.

What column is that third significant figure in? It's in the hundreds column.

Third significant figure is in the hundreds column, therefore we round to the nearest hundred.

Let's write our multiples on our number line.

We've got 60,000 and we have 60,100.

Find our halfway point and then decide where our number is and we can see that it would be to the right, and so therefore we are going to round up.

60062.

84 rounded to three significant figures is 60,100.

Your turn now to have a think about this.

Whose answer is correct? The question they are answering is round 7,003,729 to four significant figures.

Sophie says, "The fourth significant figure is 2.

I look to the right and round up, as that is a 9.

The answer is 7,003,730." Let's see what Jacob thinks.

Jacob says, "The fourth significant figure is 3.

I look to the right, I round up as it is a 7.

The answer is 7,400,000." Your turn to decide now, so pause the video, decide who is right and then come back when we can check your answer.

Who did you go with, Sophia or Jacob? It was Jacob.

Jacob was correct.

Sophia has not counted the zeroes in the hundred thousands and the 10 thousands column as significant figures.

Remember, once we've started counting, we must continue to count even if they are zeroes.

Now you are definitely ready to have a go at this independent task.

You need to decide which is the significant figure asked for in each of these numbers.

So you need to complete the sentences.

Pause the video, and when you come back we'll move on to the next question.

Good luck.

Great work.

Let's move on to question number two.

Here, I'd like you to match the following to the correctly rounded figure.

So I've given you here, whether it's been rounded to three or two significant figures, so you need to match the left to the right.

Pause the video and again, come back when you're ready.

And question number three.

We're now going to round each of the following to the number of significant figures given in the brackets.

Good luck.

Pause the video and then we'll be ready to check your answers when you come back.

Super work.

Let's check those answers.

Question number one, A was 2, B was 8, C was 3, D was 5, E was zero, F was 7 and G was 8.

Question number two, 87,995 was 88,000 to three significant figures.

Or you may have chosen 88,000 to two significant figures.

86,942 is 87,000 to three significant figures.

88,145 is 88,000 to two significant figures, and 87,492 is 87,000 to two significant figures.

How did you get on with those? You'll have noticed that if you matched 87,995 to 88,000 to two significant figures, then you would've had one without a partner.

And then question three, part A, 1,700.

B, 1,670.

C, 24,000.

D, 23,900.

E, 200,000.

F, 175,300.

G, 400.

H, 410.

I, 50,000.

J, 50,400.

K, 730,100.

And L was also 730,100.

How did you get on with those questions? I knew you'd do really well because you're really good at significant figures.

Now we're ready to move on to the next learning cycle.

We're rounding to a given number of significant figures.

Basically, we've already been doing that.

We're just going to take a look at how we do it without a number line, but remember, as always, you can choose to continue using the number line if you want to.

We're going to round 5,784 to three significant figures.

We're going to put it in our place value grid.

We're going to identify the first, second and here's our third significant figure.

And it is an 8 in that column.

It's in the tens column, so we're going to round to the nearest 10.

We now look to the digit to the right, the digit in the ones column, it's less than five, therefore the digit in the tens column stays the same.

5,784 is equal to 5,780 to three significant figures.

Ensure that a placeholder is used in the ones column to maintain the place value of the eight.

Round 145,508 to two significant figures.

Put it into our place value grid.

Which column do you think the second significant figure is in? That's right, it's in the ten thousands column.

The second significant figure is in the ten thousands column.

Therefore that's what we are going to round to, to the nearest 10,000.

Let's look at the digit immediately to the right, that's the digit in the thousands column.

It's greater or equal to five, therefore we increase the digit in the ten thousandths column by one.

Giving us 145,508 is 150,000 to two significant figures.

Again, ensure that those placeholders are used in the thousands, hundreds, tens, and ones column to maintain the place value of the other digits.

Now let's try this one, 30,559 to three significant figures.

Your turn, what column is the third significant figure in this time? I know you said hundred, didn't you? There's my first significant figure.

There's my second and there's my third.

It's in the hundreds column.

The third significant figure is in the hundreds column.

Therefore we round to the nearest hundred.

Let's look at the digit to the right.

It's exactly halfway, therefore, we increase the digit in the hundreds column by one, giving us 30,559 is equal to 30,600 to three significant figures.

And again, ensuring those placeholders are used in the tens and one columns to maintain the place value of the other digits.

Let's do one together and then you'll be ready to have a go at one of these independently, which I'm sure you'll get right and then you'll be ready to move on to the last, final independent task of today's lesson.

Well done.

Round 50,608 to two significant figures.

Here's my number.

I've got my first significant figure, my second significant figure.

It's in the thousands column, so I'm gonna round the nearest thousand.

Look at the digit to the right of the thousands column, so that's the digit in the hundreds column.

It's greater than five, so we increase the digit in the thousandths column by one, therefore gonna round up, giving us that 50,608 is equal to 51,000 to two significant figures.

Now it's your turn.

Round 46,327 to three significant figures.

Use the place value grid, or if you need to draw out your number line, either is okay.

I'm gonna ask you to pause the video now and then when you are ready we'll come back and we'll check that answer.

Good luck.

Let's check that answer.

There's my number, 46,327.

I'm doing it to three significant figures.

First significant figure, second significant figure, third significant figure.

It's in the hundreds column so I'm going to round the nearest hundred.

2 is to the right in the tens column, that's less than five, so we leave the hundreds digit alone.

We're gonna round down.

So 46,327 is 46,300 to three significant figures.

Remembering those placeholders.

How did you get on with that one? Well done.

Here we've got our task and it is a cross number puzzle.

You can, if you want to, just work out the answers to the questions.

I've given you the number of significant figures in brackets that I'd like you to round it to.

If you've got access to a printer, you could print out the grid.

If not, you might decide to draw the grid out.

You're going to round each of the numbers to the given number significant figures and you're going to put them into the cross number puzzle, remembering that you put one digit in each box.

Good luck with this.

Pause the video and then we'll check your answers when you get back.

Good luck.

Let's check those answers.

One across, 9,000.

Two across, 34,600.

Five across, 8,410.

Six across, 32,000.

Seven across, 45,500.

10 across, 370, and 12 across was, let me count how many zeroes, 2,000,000.

One down was 9,080.

Two down was 300.

Three down was 693,640 Four down was 7,120.

Five down was 8,000.

Eight down was 570.

Nine down was 500.

And 11 down was 78.

Now if I went through any of those too quickly or you got a little bit confused partway through, obviously you could now pause the video and then when you've marked it you can come back.

Now let's summarise the learning from today's lesson.

Rounding to significant figures is the same as rounding to the nearest ten, hundred or thousand.

The first significant figure is the first non-zero digit.

Zeros between other significant figures are significant and should be counted.

So for example, here, 500.

500005, all of those zeros are significant because they are between other significant figures that are not zero.

If we look at the second one, 500.

5005000, the ones between the fives are significant and the trailing ones at the end are not significant.

They are not needed to maintain the place value of any other digits in that number.

Number lines and place value grids can be used to round to significant figures.

Superb work today, well done.

Really enjoyed it.

I hope you decide to join me again really soon to do some more maths.

Thank you very much for your time.

Goodbye.