Lesson video

Hello, and welcome to today's lesson on rounding to significant figures, part one, with me, Ms. Oreyomi.

You're going to need a pen and a paper or something you can write with on.

For today's lesson, a calculator might come in handy, however, it is not essential.

So if you need to pause the video now to go get your equipment and to put your phone in silent, to make sure you're not getting distracted by anything around you, then please do so.

And when you're ready, press play, and we'll start the lesson.

Okay, in this lesson, you will learn the basic definition of significant figures.

So what does that mean? You're going to find out soon, and also, you will learn how to round to at least one significant figures.

I'm really excited for this lesson, and I hope you are too.

But before we proceed, when I say degrees of accuracy, what do you think that mean? If you said something along the lines of degrees of accuracy is how precise measurement is, or the number of decimal places, the number of decimal places it has after the decimal point, then you're correct.

Because when we say three dp, like 2.

432, the 432 is how precise that measurement is.

And significant figures, well, might as well say, significant figure talks about how precise a measurement is.

So your first task is to try this five questions.

I want you to write it down in your book, actually.

So do pause the video, write those questions down in your book, and I want you to attempt them as well.

If you finished those, the questions, look at the two statements at the bottom made by these two students.

So this one reads, I think they're all to the same degree of accuracy.

And this student says, these are all rounded to different degrees of accuracy.

What do you think of these two statements? Or two things I want you to do, write this question down in your book and answer them, and then think about these two statements at the bottom of your screen after you're done with the question.

So pause your screen now and attempt the task.

Okay, we're now going to go for our answers.

And if you struggled with this task or you've got stuck, you're not sure what to do, then I'll suggest you watch the previous video on rounding and as I think that would give you the foundation you need to be able to answer this questions.

So let's go with the first one, 745 rounded to the nearest what would give us 700? You should have written 100 because if we round it to the nearest 100, I'm looking at the 10s value, which is four.

And since that's less than five, I'm going to be rounding down to 700.

For these two statements, we will come back to these two statements in the lesson.

Okay, so what do we mean by significant figures, say in real life, I want to measure this line A, B right from A to B to centimetres, measure it in centimetres.

I could never get a precise value because the more I measure, the more precise my value would be.

So significant figures tells us how precise the measurement is.

So take for example, the first time I am measuring this line A,B over here, and I want to know the measurement in centimetre.

First measurement I take could be somewhere between 42 and 43, so I can approximate that because it's closer to 43, I could say it's going to be 42.

7.

That's what it looks like here, 42.

7 centimetre.

Now, if I stop here, I would say my first measurement has three significant figures, okay? But if I keep measuring again, I could see that I can get a more precise value.

I could get a precise measurement for what this line A, B could possibly be.

So now, I'm seeing that it is closer to 42.

7, but it is not 42.

7 nor is it 42.

65.

So I could say, approximately it could be 42.

68 centimetre.

Now, I have four significant figures, one, two, three, four.

So because I have taken a more precise measurement, my significant figures also increase.

If an even more precise measuring.

So if I take a third measurement somewhere around here, I could see that, Oh, now it's somewhere between 42.

68 and 42.

685.

So you could perhaps be again, I'm still approximating, it could perhaps be 42.

683, maybe centimetre, now again, because my precision is more, I have an even better precision.

I now have five significant figure, and I could keep going on and on, but I come to a point where I to stop because I can't ever get a perfect measurement.

So I would say that I stopped at five significant figure, that the precision of my measurement is at five significant figures.

And that is what significant figures help us to know, where we stopped taking the measurement or where we stopped rounding up.

Okay, we're establishing the last slides that significant figures tell us the accuracy of a measurement, they tell us where we stopped, where we took our measurements.

So let's discuss this precision, let's discuss this accuracy.

We've established again from the last slide that 47.

84 centimetres has got four significant figures.

And the four significant figures are one, two, three, and four.

So the 47 and 84 are the significant figures, four of those.

If we have a number like 0000047.

84, these zeros here do not add anything to our precision.

They do not tell us how, whether we've taken a more precise value or less precise value, and they do not therefore count as significant figures.

So if we have a zero before a number, they do not count as significant figures.

What of this example 47.

840, this zero at the end here adds a greater degree of precision, so it's not just 47.

84, but now, we have three decimal points after three decimal numbers after our decimal point.

So this zero is, I don't know, greater degree of precision, so we count that zero at the end.

So now, it is five significant figures.

What of this one, 47.

00084.

So we've got our 10s, our 100s, our 1000s and so on and so forth.

So again, it's adding the zero in this case adds greater degree of precision, so by yourself and in your book, how many significant figures does these numbers have? So how many significant figures does this number one have? How many significant figure does this number have? And how many significant figure does this third one have? 30 seconds, and then let me know what you come up with.

I'm just going to change the colour, so you can pause the screen and tell me what answer you come up with.

Okay, for the first one, because the leading zeros do not add anything to the precision, it has four significant figures, and we can write significant figure in a short form as s.

f, okay? Now, the second one, one, two, three, four, five, so here, we have five significant figures.

What of this last one here, we have one, two, three, four, five, six, seven, greater level of precision.

So it's seven significant figures.

So essentially, if there's a lead in zero before the start of our number, it doesn't count as a significant figure.

However, if there is zeros at the end of our numbers after a decimal point, then it counts as a significant figure.

And if there's zeros in between our numbers, then it counts as significant figures, Okay, so now, let's go back to our start with task.

I'll try this task.

Let's go back to the two statements our students are saying, this student saying, I think they're all to the same degree of accuracy.

This students saying, they're all rounded to different degrees of accuracy.

I've written out the bottom, they're both correct.

But why do you think they're both correct? Let's start with the student on the right.

They're all rounded to different degree of accuracy.

They are, they are all rounded to different degrees of accuracy, the first one is rounded to 100s, tens of thousand, 10s into just that whole number and 1000, he's correct.

But our second student is also correct because, exactly, they all round to one significant figure.

In this first number over here, I'm just going to get my pen, seven.

There's only one significant figure here, and that is seven because these zeros, zeros at the end, they do not add to the precision.

It's just one significant figure, which is seven.

In this case, although they are food zeros, they do not add to the precision, so it's just one significant figure.

Again, just one significant figure, one significant figure and one significant figure over here.

So both students are correct.

In one case, they're all rounded to different degrees of accuracy in terms of 10s, 100s, tens of thousands and so on, and another case, they're all rounded, they're all to the same degree of accuracy because they all have one significant figure.

Okay, let's look at this question.

Round 502.

67 to the nearest integer.

If I want to run this number to the nearest integer, it is closer to 503, 503, than it is to 502.

So I am going to write 503 here.

Now, let's look at the second question.

Round 502.

67 to three significant figures.

So our number must have three significant numbers.

So let's look at, we start counting from our first non zero digits.

So five is a non zero digit, so I'm going to write that down.

Zero, since it's not the first number counts as a significant number, so I'm going to write zero here.

Now, pause, I've got 2.

6, six is greater than five, so I will be rounding this number up to three.

So my 502.

67 round into three significant figure is the same as rounding 502.

67 to the nearest integer.

Let's try another one.

I want to round 40.

9 to the nearest integer.

Take some time, try to do this yourself.

Pause the video if you have to, and then we'll come back and work through it together.

Okay, 40.

9 to the nearest integer.

Again, 40.

9 is closer to 41 than it is 40, so rounding 40.

9 to the nearest integer is going to give me 41.

Now, I want to round 40.

9 to two significant figure.

So I want two significant numbers.

So 40 is a non zero digit, so I'm going to write it there.

Now, I've got 0.

9, this nine here is greater than five, so I'm going to round my zero to one.

So 40.

9 to two significant figures is 41.

The same as rounding 40.

9 to the nearest integer.

Okay, let's take a look at the three questions on your screen.

We're told to round 12,567 to three significant figures.

It is firstly very important to note that this is 10,000.

So the value of number is 12,567.

So whatever we round, it's going to be in that same value of the 10,000 range.

So we want to round to three significant figures.

First number is a one that is a significant number, I am going to write it down.

Let's look at our second number, it's a two, I am going to write it down.

Now, because we're rounding to three significant figure, I will be looking at my fourth number, in this case, that is a six.

And because six is greater than five, I will be rounded my five up.

So it's going to be 12,600.

So I'm going to replace the six and the seven with zeros.

So 12,567 to three significant figures become 12,600.

Okay, let's look at our second example, round 4507 to two significant figure.

Again, this four here tells us that it is 4000, 4507.

Now, I want to round to two significant figures.

So my first significant digit is the four, it is a non zero digit, so I'm going to write a four.

Now, because I'm rounding to two significant figure, I am looking at my 10s digit, which is zero.

Now, because zero is less than five, is my five going to change? Is it going to go up or down or remain the same? Yeah, it's going to remain the same.

So I'm going to write five here.

And then what happens to my zero and the seven? They get replaced with zero.

In this number, what are my two significant digit? Yeah, four and five.

Let's try the last one, round 5601 to one significant figure.

So I will be looking at my 100s value.

This six over here.

Is six because six is greater than five, what's going to happen to my 1000s value? Is it going to go up or down? Yes, it's going to go up.

It's going to get rounded up to six.

So it was going to be six.

And what happens to the rest of my digit six, zero, and one? Yeah, they get replaced by zero, so rounding 5601 to one significant figure gives me 6000.

You're now going to get a chance to attempt your independent task.

So pause the screen now and attempt your independent task.

And once you're done, come back and we can go for the answers together.

Okay, welcome back.

Let's go for the answers together, the answers are already on your screen, so you should be checking your work to make sure that you have the same thing.

And if you don't, just correct in your work.

So the first one, how many significant figure does the numbers 00.

546 have? And it is indeed three because remember we said the zeros at the start don't count.

What of this one? Again, it would be two, just the four and the five count as significant figures.

What of this one? It'd be four, one, two, three, four because remember, we said if it was a zero at the end of a decimal point, then it counts as significant figure because it's given us more precision.

It's given us a more precise value, it's one, two, three, four, five, six.

Okay, next question, how many significant figures does 500 have? We know that it has one because only the five counts as a significant figure and the zeros do not count as significant figure because they are not adding any sort of precision to our number.

Round in 567.

5 to the nearest integer is the same as rounding to three significant figures because if we round this number to the nearest integer, it gives us five, six, eight.

And if I ran the same number to three significant figure, I get five, six, eight as well.

This one rounding 60.

9 to the nearest 10 it's the same as rounding to one significant figure.

And if I run this number to three significant figure, I would have, this should be a zero here.

I would have 5610.

Remember, the five is telling us that it's in the 100s range.

So I should have 5610.

And if I round to one significant figure, this becomes a zero, zero, so it becomes 200.

Okay, I'm going to be helping us with this second example here.

So 5007 round it to a certain amount of significant figure, it's the same as rounding to the nearest 10.

If are around 5007 to the nearest 10, what number do I get? 5010, so if I round this to three significant figure, I'll be looking at this number here 'cause it's the fourth digit.

So it's going to be 5010, 510, the same as rounding to the nearest 10, which is going to give me 510.

So now again, pause the video and use the example number two, to help you to work the rest of the questions on your screen.

And once you're done, press play to see the answer.

Okay, here are your answers, check your work and make sure that you understand it.

If you have any questions don't hesitate to contact your teachers and they should be able to help you.

We have now reached the end of today's lesson, again, well done for sticking through and staying right to the end.

And I hope to see you next lesson.