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 math.

Come on, let's get started.

Welcome to today's lesson.

The title of today's lesson is "Round into Significant Figures." And this is within the Unit: Estimation and Rounding.

By the end of today's lesson, you'll be able to round integers to one significant figure.

Significant figure is possibly a new term that you are not familiar with.

Familiar with yet that is I say.

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

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

Now, I don't want to spend too much time looking at that now because that's what we're going to be covering in today's lesson.

And don't worry if you're a little bit confused at the moment, I can assure you by the end of this lesson you will know exactly what we mean by a significant figure.

Round.

We are going to round numbers to significant figures and we've done lots of work on rounding recently, or you've done lots of work on rounding recently and we know that that means to change a number to another number with approximately the same value, but a value that is much easier to work with or that gives us an idea of the size of a number without knowing the exact number.

And our example here is 561 to the nearest 10 is 560.

Today's lesson is going to be split into three learning cycles.

In the first one, we're going to identify significant figures.

We're just going to concentrate on what that word significant means and what does it look like when we are looking at integers.

In the second one, we're going to be using a number line so that we can round the significant figures.

And in the final learning cycle, we will look at round into one significant figure.

Well, we'll do this in the second one, but this time, we'll do it without the means of a number line.

Let's get started on that first one, identifying significant figures.

Come on, let's go.

Izzy and Alex are discussing which digit they think is the most significant in 123 456 789.

Now, can you say that number out loud? It's a very big number, isn't it? It's 123,456,789.

Is that what you said? Well done if you did.

Izzy says, "I think the nine is the most significant as it is the highest number." Remember they're discussing which digit is the most significant.

Alex says, he thinks it is the one as that is the first digit.

One of them is correct.

Who do you think is correct? The most significant figure is the figure that shows us the approximate size of the number.

Therefore, Alex is correct.

The one in the hundred millions column tells us most about the size of that number.

The nine in the ones column tells us nothing about that size of that number at all.

"So the first digit is the most significant." So Izzy's now suggesting that that is the most significant, the first digit.

And Alex says, "Yes, I think so." So remember, Izzy and Alex are just thinking about this.

This is the first time they've seen it.

Just as this might be the first time that you've seen anything that's talking about significant figures.

Which is the most significant figure in 3,456? Three is the most significant figure in 3,456.

The first significant figure is the first non-zero.

Now that's extremely important.

The first non-zero digit in a number.

In 18, the one is the most significant figure.

In 293, it's the two.

In 5,678, the five is the most significant.

In 93,592, it's the first of those nines.

"I see what's going on here." Izzy says.

"The first significant figure in the number is just the first digit.

If I write the number, 573 like this, 0573, is zero now the first significant figure?" I'm gonna pause a moment and let you have a think about what Izzy has just said.

Let's see what Alex has got to say.

"No." Alex has remembered from the definition that we talked about at the beginning with the keywords on the last slide, that it's the first non-zero digit, the first digit that isn't zero.

And in 0573, the zero is not significant.

The first significant figure is the five because that is the first non-zero digit.

Alex is correct.

The first significant figure in an integer is the first non-zero digit.

Well done, Alex.

In which of the following is four the first significant figure? Pause the video, write down your answers, A, B, C, or D.

And there could be more than one and come back when you're ready.

Great work.

Let's have a look.

The first significant figure which one is four? And it's B and C.

The first significant figure in A is nine and in D it's five.

You're ready to have a go at task now.

So just a very quick task.

We are just identifying which is the first significant figure.

So you're going to circle the first significant figure in each of those.

And if you've not got this printed out, you could just write down what figure it is, if you wanted to or you could write the number and then circle it.

Pause the video and I'll be here when you come back to check in with those answers.

Super.

Hopefully, you found that extremely easy and you should have just circled the first digit in each of those because none of the numbers started there with a zero.

We're now ready.

Now we know what significant figures are to look at actually rounding to significant figures.

And we're going to start by doing that with a number line.

Let's take a look and see what Izzy and Alex are having a chat about now.

Izzy says, "I know that 4,567 to one significant figure is 5,000." What has Alex got to say? "That is the same as 4,567 to the nearest thousand." Let's just check that.

Let's just check Alex is right.

I'm sure he is, but I always like to double check.

Yes, 4,567 is closer to 5,000 than 4,000.

So yes, I agree with Alex.

Izzy says, "The first significant figure is in the thousands column." So we notice here, we've rounded to the nearest thousand and that's also where that first significant figure is.

So Alex now suggests that, "That means we look at the column in which the first significant figure is and then we round to that." And Izzy's response to that is, "Yes, and we are already super confident with that." And I know you are too because you've done that really well over a sequence of lessons leading up to this one.

What is 54 to one significant figure? Using the place value grid, we can see which column the first significant figure is in.

You may not need to draw out your place value grid.

You will probably know that the five is in the tens column.

So the first significant figure is in the tens column.

Therefore, we are going to round to the nearest 10.

And as Izzy said, we are super confident at this already and we know we look at the multiple of 10 below and the multiple 10 above we find the midpoint and then we decide where are numbers going to go and which is its closest to.

54 rounded to one significant figure is 50.

What is 650 to one significant figure? Again, if you need to use your place value grid to decide what column the first significant figure is in, and this time it's in the hundreds column, so we're going to round to the nearest 100.

What's the multiple of 100 that is below and above 650? That's 600 and 700.

Let's find that halfway point, the midpoint of the number line and then let's see where our number is exactly halfway in the middle.

What do we do when our number is exactly halfway? Do we round it down to the lower multiple or up to the higher multiple? Yeah, you're right, we round it up to the higher one, don't we? So this is going to round to 700.

We've already said that if it's exactly halfway, we're going to round up.

What is 2,795 to one significant figure? Pause there, just to let you have a think.

The first digit this time is in the thousands column, therefore we're gonna round to the nearest 1,000.

What's the multiple of 1,000 below 2,795.

That's 2,000 and above 3,000.

Let's find that midpoint.

2,500.

And 2,795 is to the right of that.

And so we can see that it rounds to 3000.

You'll see here, the only difference between what we were doing earlier and what we are doing now, is this new term significant figure.

We identify which column the first significant figure is in and then it's just as easy as round into the nearest 10, 100 and 1,000.

What is 772,162 to one significant figure? This time, the first significant figure is in the hundred thousands column.

So we're going to use our number line.

We're gonna do a multiples of 100,000 below.

And above, find our midway point and then work out where our value's going to go.

And we can see that this rounds to 800,000.

What about this one? What is 968 to one significant figure? Now we've done quite a few examples together, so I'm just going to pause a moment, give you an opportunity to see if you can work this one out.

Let's take a look.

We're rounding to the nearest hundreds because that's where our first significant figure is.

If we put those on our number line, the multiple of 100 below 968 is 900, what's the one above it? If I'm counting in 100, so I would go 700, 800, 900.

I wouldn't say ten hundred, I'd say 1,000.

Let's find our halfway point and then decide where our number is.

So just you need to sometimes just stop and think a little bit about what happens if you've got that nine that's going to change.

Which of the following are correctly rounded to one significant figure? Some of them are correct and some of them are incorrect.

I want you to decide which ones are correct for me.

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

Great work.

Now, let's have a look.

It was A, and it was C.

If we look at B, that would've been 10,000 to one significant figure.

And D would've been 5,000,000 not 500,000.

Now you are ready for your independent task.

For this task, I'd like you to match the following to the correct rounded to one significant figure number.

So the ones on the left, you're gonna round to one significant figure and then you're gonna match it to the correct answer on the right-hand side.

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

And question number two.

Here we go with our answers.

Number One.

3,487,925 would be 3,000,000 to one significant figure.

28,021 to one significant figure is 30,000.

28 rounds to 30.

And 348.

7925 rounds to 300.

Well done if you've got those right.

And now, we can check question Number Two.

36, the first significant figure is in the tens column, we round to the nearest 10.

The answer is 40.

832, the first significant figure is in the hundreds column, we round to the nearest 100 and the answer is 800.

3,519.

The first significant figure is in the thousands column, we round the nearest 1,000 which is 4,000.

43,867.

09.

The first significant figure is in the ten thousands column.

So we round the nearest 10,000 and that's 40,000.

And then the final one.

992,782.

The first significant figure is in the hundred thousands column.

We've therefore round to the nearest 100,000, and I'm hoping I didn't catch you out here.

You needed to do a little bit of exchanging of 100,000 for 1,000,000, and you end up with the answer of 1,000,000.

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

Now, we can move on to our final learning cycle.

We're gonna be doing exactly the same thing, but this time we're not going to be using our number line.

Let's take a look.

Round 65,784 to one significant figure.

We're going to use just our place value grid this time.

So we're going to place our number.

In which column is the first significant figure? Remember that's the first non-zero digit and that is in the ten thousands column.

So it's in the ten thousands column, we round the nearest 10,000.

Remember, we look to the column to the right, immediately to the right, which in this case the thousands column which gives us five.

This is exactly halfway.

Five is exactly halfway.

So therefore, we increase the digit in the 10,000 column by one.

We get 70,000 to one significant figure.

Ensure that the placeholders are used in the thousands, hundred, tens and ones column to maintain the place value of the seven.

It's really important.

We can't have the 65,784 to one significant figure is seven.

That's just a nonsense.

Let's try this one.

Round 1345.

02 to one significant figure.

What column is the first significant figure in? It is in the thousands column.

So we're going to round the nearest 1,000.

Let's look at the digit to the right, that's the one in the hundreds column.

This is less than five.

So we are going to leave the digit in the thousands column alone.

We are going to leave it as a one.

And then remember, we need those placeholders.

So the answer is 1,000 to one significant figure.

And again, just that note, to really reiterate that you really need to make sure that you include those placeholders.

Alex rounds 87,392 to one significant figure.

Says, "87,392 is nine to one significant figure." What mistake has Alex made? Alex has forgotten to replace the seven, three, nine and two with zeros, the placeholders to maintain the place value of that nine.

And that's a really common mistake, but I'm sure you didn't make it because I highlighted it on the previous slide.

87,392 is 90,000 to one significant figure.

We're gonna do one together and then I'm gonna ask you to do the one on the right-hand side by yourself.

Here we go.

The first significant figure is in the hundreds column.

We look to the right, it's greater than five, so therefore, we round the number in the hundreds column up one.

It'll be the value higher, so it's going to be 400.

Your turn.

Pause the video.

Write this number to one significant figure for me and then come back when you've got your answer.

Okay, let's take a look.

63.

91.

The first significant figure is in the tens column.

We're going to round to the nearest 10.

We consider the digit in the ones column, it's less than five, so we leave it, we round down to the lower value, which in this case would be 60 because we were rounding to either 60 or 70, and we've just decided that we're rounding down to the lower of them, so your answer was 60.

Did you get that right? Super, well done.

Now, you're ready to have a go at this task.

You're going to write each of the numbers below to one significant figure.

You need to find the answer in the grid to complete this joke.

So you need to work out the answers.

What I've done is I've put a box around each of the separate words.

So you'll notice that the first word is just one letter.

The second word is four letters, but you'll need to rearrange those letters.

So I've jumbled up all of the letters, but each box contains one word.

And this is the joke that you are going to complete.

"A sheepdog goes out to get the farmer's sheep in.

He comes back and says to the farmer, 'That's all 100 sheep in the barn.

' The farmer says, 'That's odd we only had 97 this morning.

' The sheepdog replies." And your job is to work out the punchline to the joke and what the sheepdog said.

So you're going to pause the video, you're going to round each of those numbers below the grid to one significant figure, and then if you can look up the letters, rearrange them to give the punchline to the joke.

Good luck with this.

Pause the video and I look forward to seeing if you laughed at the joke when you get back.

Are you laughing? Of course, you are.

Not going to reveal the answer just yet though, because there's some more questions for you to have a go at.

Question number two.

You need to decide what values the missing digit can take? So what values could the question mark be in each of the following? Pause the video and then come back when you're ready.

Super work.

Well done.

Here we go then.

So number one was 5,000.

Two, 2,000.

Three, 1,000.

Four, 70.

Five, 100.

Six, 5,000.

Seven, 70.

Eight, 10.

Nine, 800.

10, 8,000.

11, 30,000.

12, 2,000.

13, 30,000.

14, 80,000.

15, 90.

16, 10,000.

17, 10.

18 was 7,000.

And 19 was 800.

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

Obviously, if I went too fast, just pause the video and you can check those.

Let's see what the punchline then was.

I'll read out the whole joke.

"A sheepdog goes out to get the farmer's sheep in.

He comes back and says to the farmer, 'That's all 100 sheep in the barn.

' The farmer says, 'That's odd we only had 97 this morning.

' The sheepdog replies, 'I know, I rounded them up.

'" Did you get the joke? 97 rounds up to 100.

But a sheepdog also physically rounds up the sheep.

I'm really sorry if you didn't get that and you needed me to explain it, that means it was not a great joke.

Let's move on to question number two.

What values can the missing digit take? So in A, it could have been 0, 1, 2, 3, or 4.

B, could have been 5, 6, 7, 8 or 9.

C, could have been any digit.

And D, also could have been any digit.

Now we can summarise our learning from today's lesson in which you've done really well.

So we've been introduced to this new term.

For most of you, it probably will be a new term, which is round into significant figures, but we can think of this as the same as rounding into the nearest 10, 100 and 1,000.

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

So, that's really important.

We're looking for the first digit that isn't zero.

Number lines can be used to round to one significant figure.

And we used a number line here, and there's an example of when we did during the lesson.

Also, we can use place value grids to do our round into one significant figure.

You can choose between the two.

Sometimes you may prefer to use one, sometimes you may prefer to use the other, and you also may not to need to draw out either of them, but be able to successfully round to one significant figure.

Thank you so much for joining me today for today's lesson, and sticking with me and working really hard.

Goodbye, and I hope to see you again really soon.