Lesson video

In today's lesson, you will be able to round numbers to more than one significant figure.

Your first task then, is to place each of the following numbers into the place value.

So you can draw what you see on your screen, or you can draw your own version.

Your job is to put each of these numbers into the place value grid, so pause the video now and attempt the task, and when you're ready, press play to see the answers.

Okay, so on the screen we have the answer to the question, we've just replaced each of the numbers on the place value grid.

So let's look at the first one.

You've got 192.

3949.

That means we've got one 100, nine 10s, two ones, three 10ths, nine 100ths, four 1000ths and nine 19000ths.

Okay? Now, if you notice for this number here, 803.

0293.

I haven't put my zeros here.

I haven't put my zeros here.

I haven't put my zeros here.

And I haven't put my zeros here.

You might be thinking back to the previous lesson, and thinking, ah, I know why.

But if you're not sure, don't worry.

We will go over it later on in the lesson.

So just make sure you have the right thing on your sheet before we proceed to the next slide.

Okay, our first question then is to round 192.

3949 to one significant figure.

Okay? So this one here tells us that it's in the hundreds range.

So if I want to round to one significant figure, I am going to be looking at the second value here, which is the nine.

Since nine is greater than five, should I be rounding up or should I be rounding down? Exactly, I should be rounding up.

So my one becomes two.

And that is my one significant value.

However, because I am in the hundreds range, I need to stay in the hundreds range, because this is 192.

I am going to add a zero here, and a zero here as well, to show that it is in, the double zeros, two zeros show that it is still in the hundreds range.

So it is 200.

So my significant figure, my one significant figure is this two.

And the 00's are what we call place holders.

They are giving us more information about that number two.

Saying it is 200.

But the two is the significant number.

200 is 192 rounded up to one significant figure.

Let's try then, if I want to round 192.

3949 to two significant figures, what number should I be looking at? Exactly, I should be looking at this two here.

Now, because the two is less than five, what should be happening to my number? Exactly, it stays at one, nine, zero.

190, so I've got one, that's one significant figure, two, that's another significant figure.

And this two becomes a zero.

It is showing me that I am in the hundreds range still.

So it's 190.

So how many significant numbers do I have in this answer here? It would be one and two.

So round 192.

3949 to two significant figure, would give me 190.

So I'm just going to write that here.

The two, saying it is 200.

But the two is the significant number.

200 is 192 rounded up to one significant figure.

Let's try then, If I want to round 192.

3949, to two significant figures, what numbers should I be looking at? Exactly, I should be looking at this two here.

Now, because the two is less than five, What should be happening to my number? Exactly, it stays at one, nine, zero.

190, so I've got one, that's one significant figure, two, that's another significant figure.

And this two becomes a zero.

It is showing me that I am in the hundreds range still.

So it's 190.

So how many significant numbers do I have in this answer here? It would be one and two.

So, round 192.

3949 to two significant figure, would give me 190, so I'm just going to write that here.

And this one significant figure.

Okay, what of four, round up or down? You're exactly correct.

I should be looking at my ones column.

Now, since my ones column is greater than five, I will be rounding up.

So if I round two up, is going to be three.

Okay? Yes.

I've got my one significant number.

But three on it's own stays as three tens.

So what should I add to make it three tenths? A zero, right? So it's going to be to one significant, just write my S, significant figure.

Let's try round that up to two significant figures.

So I've got put a 29.

8787, 29.

8787.

If I want to round to two significant figures, which number should I be looking at to determine whether to round up or down? You're exactly correct.

I will be looking at this tenths column, 'cause that would be my third digit.

Now, eight is definitely greater than five.

So what's it going to be? Hm, again I'm rounding up.

If I round nine up, I've got 10.

So I'm going to have a zero here, and three here as well.

Now this time, because I've got two significant figure, I am going to put the decimal point at the end here, just to show that the zero counts as a significant figure this time.

So for my zero to count as a significant figure, I have to put a dot, a decimal point, at the end.

So this would be to two significant figure.

So this shows that the zero is not simply a place holder, but it is giving us a more precise measurement of that value.

Let's try round this up to three significant figure.

So again, if it's rounding up to three significant figure, what number am I looking at? Exactly correct, I'll be looking at my fourth digit here, which is the seven.

Because seven is greater than five, I will be rounding up, exactly.

So I'm going to have 29.

9, 29.

9 would be my rounded up values to three significant figures.

You see how for each one, this gives me one significant figure.

So I've got this one non-zero number.

That is one significant figure.

Now this one, I've got one, two significant figure, and the zero counts as a significant figure because I've put a decimal point at the end.

If I do not put a decimal point, it is simply one significant figure.

With this one I've got 29.

9, and I've got one, two, three significant numbers.

Now what of this one, five, 50.

0009.

50 is five tenths, zero ones, zero tenths, zero hundreds, zero thousandths and nine 90000ths.

Try and tell me, what is the difference between 05, what is the difference between 050 and 50.

0? Well for starters, this zero does not really add any importance, any value to the number.

050 is still 50.

So that's why leading zeros does not count as a significant number, because it does not add anything to it.

Now these zero at the end without a decimal point, I could have rounded up from 45.

I could have rounded down from 54.

So the zero does not count as a significant number because it's not telling us the precise value.

However, if I've got 50.

0009, it's saying this is a greater precision number.

This is a greater precision measurement.

That is why the zeros after the decimal point and the zeros in-between numbers, so in-between five and the nine, they all count as significant numbers.

Now, if I want to round this number to one significant figure, which number am I looking at? This here, so it's simply going to be 50.

Do I need to put a decimal point at the end of the zero here? No, because I only want one significant figure.

Okay? So it's just going to be one significant figure.

Okay, what if I want to round to, this is a decimal point, what if I want to round to two significant figure? What's it going to be? Good, it is simply going to be 50.

What must I put to show or to make my region know that the zero counts as a significant number? Correct, I must put a decimal point here to show that the zero is part of my precision measurement.

And this would be to two significant.

Okay? What if I want to round the same number to three significant figures? So now this time I want three significant numbers in my answer.

It's going to be, I'm looking at the fourth digit, zero, It doesn't go up.

It doesn't go down.

It just stays the same.

So it's going to be 50.

0.

Correct, Two significant value, the third significant value.

So it's going to be three significant.

How 'about you try this yourself? What would you get if you round 0.

051 to one significant figure? And 0.

052 to two significant figure? Pause the video and then come back, and let's work through it together, after you've had a chance.

Okay, if I want to round 0.

051 to one significant figure, I am looking at this number here, because that would be my first significant number.

Remember we said the leading zeros before a non-zero digit number does not count as a significant number.

So these zeros one and two, does not count as a significant number.

So 0.

051 to one significant figure would be 0.

05.

And what would be my significant figure here? What would be my significant number here? It would be five.

That would be my only significant number.

So I'm just going to write, I rounded that number to one significant.

Okay, what if I then want round 0.

051 to two significant figure? I want two significant numbers in my answer.

Well, what are the only two significant numbers in this value? You're exactly right.

Five and one, so it's going to stay the same.

It's going to be 0.

051.

And my two significant numbers are five and one.

Okay, you're are now going to get a chance to work through the independent questions.

So I want you to pause the video now, try to complete the questions.

And then once you're done, come back and we'll go through the answers together.

Okay, let's look at the answers to our questions.

We were told to round 0.

0882 to two significant figures.

We only want two significant numbers, and there is a eight, an eight.

So that'll be 0.

088.

Checking your work, making sure you've gotten that, right? This one, they put lots of zeros there.

I think they're trying to mislead us, but we know that leading zeros, they don't add to the precision.

They don't add to the significance.

So to three significant figure, we're looking at this number here, to see whether to round up or down, because it is a three we round down.

So it's going to be 0.

00017 and eight.

So my three significant numbers here are one, seven and eight.

Round 9.

99 to one significant figure.

I am looking at my second number.

My second number is a nine.

I've got nine tenths, and I'll be rounding that up to 10.

So the only significant number in this, in 10, is one.

Round 85562 to three significant numbers.

I have got eight, five, five.

However, I'll be looking at this six to see whether to round up or down, because it is a six I round up.

So it's going to be 85600.

Remember earlier in the lesson, we said, we put the 00 to show place holders, so they're place holders.

I'm just going to write P H.

They're place holders, just to show that it is 85600.

Because if we leave, if we don't put the zeros, it's going to change.

Our answer is simply going to be 856, but that was not the number we started with.

We started with a number in the 80000's, and this shows us that, this is 85600.

And again, 60.

0041 to four significant figures.

So we've got one, two, three, four, I look at this four to determine whether to round up or down.

Because four is less than five, I round down.

Now to show, because the zeros are in-between six and four, they count as significance figures.

So just to recap, if the zeros are in-between non-zero digits, they count as significant figures.

Next question.

At a festival there were 6727 people and we're told to round to one significant figure, and that is 7000.

And the only significant number here is seven.

Again, a supermarket sold 5872 toilet rolls.

The manager rounded this number to two significant figure.

So for this one I am looking at the seven, to determine whether to round up or down.

Seven is greater than five, so I will be rounding my eight up.

Don't forget your place holders here, to show the value of your number, in the five thousands, 5900.

Okay, James has worked out the answer to a calculation.

His teacher told him to write all his answers to four significant figures, round his answers to four significant figures.

Significant number one, number two, number three, this is my fourth significant number, but I'm looking here to determine whether to round up or down.

Six is greater than five.

So I'll be rounding up.

So this answer rounded up to four significant figure, is 723.

6.

Okay, onto your Explore task.

Your task is to sort 0.

6248 to this given degree of accuracy.

And after you've sorted each one to the first one, to one significant figure, second one to one decimal place, and so on, then you are asked to sort it into ascending order.

And then your second task is to write a number, when you round that number up to three significant figure, it would become the biggest number.

If you round it to six decimal place, it will become the middle number.

And if you round it to two significant figure, it would become the smallest number.

I want you to pause this video now and attempt the task.

And if you do attempt it and you're struggling with it, then carry on playing the video, and I'll provide you with more help.

You, I have rounded the given values, 0.

06248, to this given degree of accuracy.

So if we do the first three together, 0.

06248, rounded to one significant figure.

So we only want one significant number in our answer, and that significant number in this case is a six.

Okay? And in this one, if we're rounding to one decimal place, 0.

0, 0.

1 rather, so we just want one number after our decimal point.

And because this six is bigger than five, this six over here is bigger than five, we'll round it up to one.

So this zero becomes a one.

And then rounding 0.

06248 to the nearest integer.

It is closer to zero than it is one.

So we round down to zero.

So, now your task is to sort these into ascending order.

For this one, and the number I've thought of is 0.

07218534.

Your job is to round this up to three significant figure, to six decimal place, and then to two significant figure as well.

And see if you're able to make it the largest value, six decimal places, the second largest value, that's two significant figures to the least.

So pause your video now and continue attempting the Explore - Okay, you have your answers here.

If I sort it into ascending order, that means it's going from the smallest value to the largest value, is, you should have gotten this.

And then if I round my number to three significant figures, 0.

722 to six decimal places, it's a bit less than 0.

722, and if it's two significant bigger it is 0.

72.

So the first one is my largest number, second largest and third largest.

Really well done for sticking through to the end and completing this task.

Make sure you show your work to your teachers, show up how excellent you've worked.

And I will see you at the next lesson.