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 Rounding Decimals to Significant Figures and that's in our unit, estimation and rounding.

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

Up until now, we've been concentrating on looking at integers and rounding integers to significant figures.

But you know how to round a decimal places.

You know how to round the nearest 10, you know how to round the nearest 10th, so you are going to be really good at this.

You've got all of the skills.

We just need to make sure we understand what it's going to look like in this context.

Keywords for today's lesson are significant figures.

Remember, those are the digits in a number that contribute to its accuracy.

The first significant figure is the first non-zero digit, and when we round, we round, we change the number to another number that's approximately the same value, but makes it easier to work.

With today's lesson, we've split into two learning cycles.

On the first one, we'll concentrate on using a number line.

You're really, really competent with using number lines now and then we'll look at rounding decimals to significant figures without a number line.

Let's get going on that first one.

So we're going to start with using a number line.

The average width of a human hair is 0.

009 centimetres.

Which digit is the most significant? It tells us the most about the size of the number.

I'm gonna pause a moment and give you a chance to think about that before we see what Izzy and Alex have got to say.

Izzy says it is the nine.

It is the only digit that tells us anything about the width of the hair.

Alex is now he's a little bit confused by the looks of it, says when we rounded numbers larger than one, the first digit was the most significant.

Why has the rule changed? So Alex is remembered that it was the first digit when we were looking at integers.

Here is not the first digit, it's not the zero, it's the nine that is in the thousandths column is his responses.

Actually Alex, if you remember it was the first non-zero digit, not just the first digit.

It isn't really any different.

Why might Izzy say that? Let's take a look at why Izzy might say that.

We could write any number with zeros in the unused columns.

So Izzy's suggesting that actually any number, because we've got zero hundreds or we've got zero millions, we could write zeros in them, but we don't necessarily need to all of the time.

Alex says, ah yes, of course we could write 60 as 0060 because there are no hundreds or thousands.

Yes, in numbers greater than one, we can leave off the leading zeros.

So up until now we've talked about trailing zeros.

The zeros at the end of a decimal after the decimal point, the trailing zeros, we call these leading zeros.

The zero zero at the beginning of 60 are leading zeros.

We don't need to write them, but in numbers less than one, we have to include those leading zeros.

Yes we do, because otherwise the place value would not be maintained of the other digits.

Let's take a look.

We could write 60 as 0000060 because I've got zero millions, zero hundred thousands, etc.

and we can now see that actually this is the first non-zero digit.

It's exactly the same, but it's just that we don't see those leading zeros.

When rounding to significant figures, the first significant figure we know is the first non-zero digit in a number.

For example, 0.

00483.

The four is the first significant figure is the first digit that isn't zero.

The first non-zero digit.

0.

083904, the eight is the first significant figure.

1.

00398, the one is the first significant figure, the first digit that isn't zero.

In 0.

00023, it's the two.

In 310.

952, the three is the first significant figure.

In which of the following is four the first significant figure? Pause the video and when you've got your answer, A, B, C, or D, it could be more than one, come back and we'll check.

What did you decide? I hope you've said B and you've said C.

A, the first significant figure is the two.

And D, the first significant figure is the six.

What is 0.

123 rounded to one significant figure? Think back to what we did when we did integers.

We've put it into our place value grid so we can see which column we are looking at.

Our first significant figure significant, remember, is the first non-zero digit.

That's not significant because it is zero.

Here is my first significant figure.

It's in the tenths column.

So therefore we are going to round to the nearest 10th.

We need to write our tenths either side of 0.

123 on our number line, which are 0.

1 and 0.

2 and then we find the halfway point.

Remember, if you're not sure, find the sum of the two values and then half it and you'll get 0.

15.

Let's place our number onto the number line and we can see now that it is closer to 0.

1.

0.

123 is equal to 0.

1 to one significant figure.

Now we'll take a look at this one, 0.

0068.

Again, to one significant figure.

Here it is in my place value grid.

Which column do you think the first significant figure is in? Well done.

Yeah, you are right.

It's in the thousandths column, isn't it? Not significant because it's zero.

Not significant, not significant, first significant figure.

It's in the thousandths column, we're going to round to the nearest thousandth.

Let's put this onto our number line.

It's just gonna be 0.

006 and then remember the other end we are going to increase the thousandth digit by one given a 0.

007 and then we're going to find that halfway point.

We then need to place our number, 0.

0068 is greater than 0.

0065.

We can now see which is closer to 0.

0068 is equal to 0.

007 to one significant figure.

Now let's take a look at this one.

Which column is my first significant figure in? Yeah, that's right, it's in the hundredths column.

The hundredths column.

The digit in the ones column is a zero, not significant.

In the tenths column is a zero, not significant.

Here then we're going to round to the nearest hundredth.

Let's place that on our grid or our number line I should say.

So we've got 0.

09 and then we need to add on a hundredth given us 0.

1.

Find the halfway point and then decide 0.

096 is greater than 0.

095.

We can now see that it rounds to 0.

1 to one significant figure.

Let's look at a different number of significant figures now.

So up until now we've been looking for just one significant figure.

Let's have a look at three significant figures.

We've got 10.

392.

First significant figure, remember once we start counting we need to continue.

So that's our second, even though it's zero.

And then our third.

It's in the tenths column, so we're gonna round to the nearest 10th.

Let's go a 10th below, which is 10.

3 and to the 10th above, 10.

4, find our halfway point and then decide where our number goes on our number line, which is roughly there.

Remember it doesn't need to be exact.

That means 10.

392 is equal to 10.

4 to three significant figures.

Your turn now.

Which are the following are correctly rounded to one significant figure.

So some of them are correct, some of the incorrect.

So identify the ones that are correct and maybe the ones that are incorrect, you could correct those.

Pause the video, good luck.

And when you come back we'll check those answers.

Great work, which ones did you decide on? The first one is not right, okay.

To one significant figure it would be 0.

3, but B is correct and D is correct.

C, in case you've rounded it to one significant figure, it would've been 30.

Independent task now.

This question I'd like you please to circle the first significant figure in each of the following.

Pause the video and then when you come back we'll move on to the second question in this task.

Great work.

Question number two, you need to match the following correct number rounded to one significant figure.

I've rounded them all to one significant figure and you need to match it up to the correct one on the right hand side.

Again, pause the video and come back when you're ready.

And question number three, you're going to round each of the following to the number of significant figures given in the brackets and you've got different numbers of significant figures there.

So just take care to make sure you've carefully looked at how many significant figures you are going to do for each one.

Again, pause the video and I'll look forward to seeing you when you get back.

Well done.

Let's check those answers then.

So one A, it was the four, B was the five, C was five, D was the first one, E was nine, and F was one.

Onto question number two, 0.

0001492 rounds to 0.

0001, 0.

0971 rounds to 0.

1, 0.

001093 rounds to 0.

001, and 0.

0095028 is equal to 0.

01.

Question number three, here are your answers.

A, 0.

0009, B, 230 C, 0.

824, D, 1000 E, 0.

01, and F 0.

02380.

How did you get on with those? Of course you got them all right, well done.

I knew you would.

Now we're ready to move on to the final learning cycle for today's lesson and we're gonna stick to rounding decimals to significant figures, but we are going to try it without drawing the number line.

We are going to round 0.

000642 to two significant figures.

Let's put it into our place value grid.

Right, over to you.

You tell me in which column is the second significant figure.

Yeah, first significant figure is in the 10000th column and the second is in the hundred thousand column.

We're gonna round to the nearest hundredth thousandth.

Let's look at the digit to the right immediately to right.

In this case, that's in the millionth column.

It's less than five, so we don't change the digit in the hundred thousandth column.

Okay, it stays the same.

Our answer therefore is 0.

00064.

and this one 0.

000095.

Hope I said the right number of zeros there.

Let's put it into our place value grid.

We're doing this to one significant figure.

Where is my first significant figure? In which column? It's in the hundred thousandth column.

We're gonna round the nearest hundred thousandth.

So we're gonna look at that digit in the millionth column and that's a five.

Exactly halfway.

What happens when we're exactly halfway? Do we round up or down? Yeah, well done.

We round up, don't we? Therefore, we're gonna increase the digit in the a hundred thousandths column by one.

Our answer here is 0.

001.

Just take care there.

When you increase nine, you get 10.

But remember you will be exchanging your hundred thousandths for a 10000th.

So that's why the answer is 0.

0001.

Let's take a look at this one, 0.

06076.

Place value grid, three significant figures.

First, second, third.

It's in the 10000th column this time, so we're gonna round the nearest 10000th.

Let's look at the digit to the right, the one in the hundred thousandth column, the column immediately to the right.

It's six is greater than five, so it's greater.

So we are going to round up, we increase the digit in the 10000th column by one, giving us 0.

0608 to three significant figures.

Notice that the zero between the six and the seven is significant.

Once we start counting, we must continue.

Izzy and Alex are rounding 0.

00300858 to three significant figures.

We need to know who is right.

You need to decide for me who is right.

Also, what mistake has the other person made? Let's see what they've got to say.

Izzy's answer is 0.

0030086.

And Alex's answer, he says he thinks it's 0.

00301.

Pause the video, decide who you agree with, and then also try to decide which mistake the other person has made.

Who do you think is right? It's actually Alex.

The mistake that Izzy has made is Izzy has forgotten that the zeros after the first significant figure are significant.

The zero in the hundred thousandths column is the third significant figure.

Once we start counting, we must continue to count and here we are with our final task for today's lesson.

You've done fantastically well up until now.

Just one task to finish.

If you've got access to a printer, you might decide to print this grid off.

You might want to draw it out or you may decide that actually you're just going to answer the questions.

I am asking you to round each of these to either one, two, or three significant figures, and you can see the groups that I've put them into.

If you are going to do the the number grid, you just need to then like a word search, but a number search.

Find each of the answers in the grid.

Pause the video now.

Hope you enjoy this task, and then when you get back, we'll check those answers for you.

Good luck.

Well done.

Let's check these answers, shall we? Here we go.

The one significant figures one, ones.

One, 0.

04.

Two, 0.

0007.

Three, 500.

Four, 0.

00007.

Five, 0.

0009.

Six, 0.

7.

And then onto the two significant figures.

One, 0.

0043.

Two, 0.

0042.

Three, 0.

52.

Four, 0.

61.

Five, 1.

4.

Six, 0.

0032.

Seven, 0.

0000073.

Eight, 0.

0072.

Nine, 0.

46.

Ten, 0.

00016.

Eleven, 82000.

And then onto the final section, which was the three significant figures.

One, 0.

906.

Two, 0.

0633.

Three, 0.

0607.

Four, 0.

829.

And five, 0.

00906.

How did you get on with those? There were lots there.

Well done if you got all of them right.

If you were there, went on to find them in the grid, here are your answers.

So if you want to check those and check that you've got them all correct.

Pause the video now and then when you are ready, you can come back and wait to make a summary of what we've done during today's lesson.

You've done really well, so pause the video if you need to, and I'll be here waiting when you get back to do that summary.

Let's summarise now the learning we've done in today's lesson.

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

That's really, really important, isn't it? But remember, zeros after the first significant figure are significant.

I've said it a lot today.

Once we start counting, we continue to count.

A number line is useful when we round decimals to significant figures, and we can see there a copy of one of the examples that we use during today's lesson.

Also, a place value chart is another really good way of working out what decimals are rounded to significant figures.

Remember, really it's just the same as rounding to the nearest 10th, hundredth, thousandth, et cetera.

Super impressed with what you've done today and I'm so glad that you decided to pop by and join me with some really good maths learning.

Well done and thank you again, and I look forward to seeing you again soon.

Goodbye.