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Hello, and welcome to another lesson with me, Ms. Oreyomi.

Today's lesson is on rounding from a calculator and also approximation.

So for today's lesson, you will definitely need your calculator.

You will need a pen and a paper, or something to write with and on.

And you would also, it would also help if you minimise disruptions or, you know, something that could distract you.

So if it's your phone, make sure you put it on silent.

So pause the video now and go get your equipment, and also, very importantly, your calculator.

Okay, let's begin.

At the end of this lesson, you will be able to know and use some features on your calculator.

You will also know what it means to approximate.

And you would be able to use your knowledge of approximation to solve complex calculations to get approximate answers.

Let's move on to our try this task.

This symbol, this calculator symbol here, means that you are allowed to use a calculator.

And I just want to show you a feature that could really help you in this task.

On my screen, I've got 12 over seven.

If you want to find the answer in a decimal form, you press this S to D button on your screen, and it should give you the answer in decimal form.

So it takes it from fraction to decimal.

So if you need to find a decimal form, just press the S to D button, which is here on your screen.

So you have four questions now.

I want you to pause your screen, and pause your video and get on with the task here.

We are now marking our work.

So the first answer has been put up for you.

Using your calculator, you're told to round one over seven to four decimal places.

That means exactly as that answer shows, we should have four numbers after our decimal point.

So right here, I should have four numbers after my decimal point.

One, two, three, four.

Use a calculator to find the decimal value of two over seven, three over seven, four over seven, and five over seven.

Okay.

Now, we're told to round two over seven to two decimal places.

So we should have how many numbers after our decimal place? Exactly, two.

But because this is a five, what's going to happen to the eight? It should go up.

So round two over seven to two decimal places, we're going to have 0.

29.

And if we do the same for three over seven, four over seven, and five over seven, what do you notice about these numbers? Yeah, you should have written that they all end with a 29 when they're rounded up to the given decimal place provided in question three.

Very good.

Now, let's look at this symbol over here.

What does this symbol mean? It's got two squiggly lines.

What do you think it means here? It almost looks like an equal sign.

What does it mean? Yeah, it means it's approximately equal to.

So whenever you see these two squiggly lines, it shows that two numbers are roughly equal, but they are not exactly equal.

So this is very different to the equal sign, which you've seen quite a lot.

So it means they're roughly the same, but they're not quite the same.

So for example, if I say 4.

5 is approximately equal to five.

5 is not five, but it's approximately equal to five.

If you remember from last lesson, rounding makes a number easier to read.

So instead of saying 4.

25, I can round up to one decimal place and say 4.

If we think back to our first task, where we were rounding the right of the decimal two over seven, three over seven, four over seven, five over seven, you should have noticed that each fraction is leading us closer to, I've just put the fractions here, each decimal rather, or each fraction is leading us closer to which number? Exactly, one.

Each fraction is leading us closer to the number one.

We're getting closer to one each time, 0.

1, 0.

2, 0.

4,.

5,.

If I do six over seven, I get 0.

85714489 to eight decimal place.

I could say this number is approximately equal to 0.

9, And if I round up 0.

9 to the nearest integer, I would get one.

So seven over seven is one.

So this is when we use the approximate symbol, to round up a number, to say it's almost equal to another number.

An approximation really comes in handy when we're in the supermarket, for example, and they're doing a 17.

5% sale, we can just round it up to 20% or to 18%, to a nicer number that can help us to work out complex calculations.

And we're going to see how that works now.

So look at this first question.

I've got root 25 plus three squared plus six.

I know that route 25 is what? Exactly, it is five.

And three squared is what? Yeah, three squared is nine.

And then plus six.

My answer should be: five plus nine plus six is 20.

Okay? That was very straightforward.

Let's try another one, which is there.

Let's try another one.

Just going to rub that 20 out so you can see it better.

I've got root 27 plus 3.

1 squared plus 8.

96.

What do you notice about this question here and this question here? The numbers are very similar.

Now, off the top of my head, I don't know what root 27 is.

But I know that it is between root 25 and root 36.

Which one is it closer to? Root 25.

So I am going to approximate root 27 to be five.

And then 3.

1 squared, again, off the top of my head, I don't know what 3.

1 squared is, but I know that I can round down to three.

So I'm just going to run this down to three again.

So again, three squared.

89.

I could just round this down to the nearest integer, which is going to give me six.

Do you see now how rounding calculations that I don't know the precise answer to can make my calculations really easier.

So I've gone from root 27 plus 3.

1 squared plus 5.

89 to five plus three squared plus six, which should give me the same answer as I go over there, which is 20.

Now, we know that this is not the precise answer because we have approximated.

So now take a calculator, and I want you to type these into your calculator and tell me what you get to the nearest, to one decimal place.

So type this values into your calculator and tell me what you get to one decimal place.

And I'm going to do the same as well.

What did you get? I got 20.

7 to one decimal piece.

Do you see how, using an approximation, I got a number very similar to the exact value.

So approximation helps us to get a value, an answer, similar or approximately to our value.

Let's look at this question.

I've got cube root of root 63 plus 82 divided by 5.

74.

I don't know what cube root of 63 is.

However, I can approximate 63 to 64 because I know what the cube root of 64 is.

So over here, I'm going to write again using my new approximated values.

So over here, I'm going to write cube root of 64 plus, now 82, because the value is less than five, I am going to round down to 80.

Okay.

And that should be a straight line.

74.

I want to round it to the nearest integer to make my calculation easier to do, so I am going to round it to six.

Now, let's try it.

Let's try and do this by ourselves without using a calculator.

Cube root of 64 is four plus 80 divided by six.

80 plus four is 84 divided by six, knowing that from your timetable, we know that it should give us 14.

Okay? Now, let's put that value, let's put the exact thing.

Cube root of 63 plus 82, all divided by 5.

74, and see what we get as our exact answer.

So you do it as well with your calculator.

We got 14.

9, approximately, which could be rounded up to the nearest integer as a 15.

So putting the exact value, I get 14.

978, and if I round this to the nearest integer, I get 15.

So we are going to say, this is approximately, I'm not saying equal to this time, I'm saying it is approximately, I'm pretty sure your approximately symbol would be so much better than mine.

Just to remind you that this is the approximately symbol.

So this calculation is approximately equal to 14.

It is not 14.

I'm just saying, doing this off the top of my head, without using a calculator, I would estimate, I would approximate, that this calculation would give me the answer 14.

And putting it into a calculator, we got the answer 14.

Let's try this next one approximating.

46.

If I want to round 6.

46 to the nearest integer, because this is less than five, I am going to round down to six.

012.

Again, I want to round to the nearest integer.

So I'm going to make this nine.

You do the next one.

56.

If I want to round 2.

56 to the nervous integer, what does it become? Exactly.

It becomes three.

Six times nine divided by three, so we know that this is 54 divided by three, and you should have gotten 18.

54 divided by three is 18.

So using my calculation, I am going to write that 6.

46 times 9.

012 divided by 2.

56 would give me an answer approximately equal to 18.

Let's put that in our calculator to see if we are close.

I want you to be doing the same on your calculator as well.

So you can pause the screen to check.

When I typed this in my calculator, I got an exact answer of 22.

74.

So if I round up to one decimal place, this is going to give me an answer of 22.

This is interesting.

Approximately, my answer is 18, but my exact value is 22.

Can you think about why that might be? Yeah, it has to do with the fact that we rounded down the first two numbers.

When I round down, usually my approximated answer would be lower than my exact value.

So even though I rounded this 2.

56 to three, because I would.

I rounded 2.

46 to six and 9.

012 to nine, it makes the answer my approximate value smaller than my exact value.

Excellent.

I want you to pause the video now and complete your independent task.

Once you've completed your task, you can come back here and check your answers as well.

But make sure you complete the task as much as you possibly can before you come back to check your answer.

So pause the video now and complete your independent questions.

Right.

Yeah, you should be checking your answers now.

I want to specifically focus on B.

So we've got cube root of 8,004 plus square root of 98.

7 divided by 5.

03.

Now, I know, or I should know, that the the cube root of 8,004 is 20.

So I am going to approximate this to 20 'cause I'm going to round down.

If I round down, it's going to be cube root of 8,000, which is going to give me 20.

Plus 98.

If I round to the nearest 10, this is going to give me the square root of a hundred, which is 10.

And then 5.

03.

If I round down to the nearest integer, this is going to give me five.

So I'm going to divide that by five.

So 20 plus 10 is 30, and then divide that by five, that's going to give me approximately six.

I want to show you in case you do not know how to use this feature, the cube root feature, on your calculator.

I want you to press the shift button, which is over here.

So press the shift button over there and press the square root button as well.

So once you've pressed your shift button, then press your square root button.

That should bring up the cube root button on your calculator.

So let's see what our exact value would be.

So 8,004 plus square root of 98.

7 divided by 5.

03, And that gave me an approximate answer of 5.

95.

Round that up and we get six.

So that was quite a nice question.

Okay, let's look at D.

The question asks, Cala wants an approximate value for 9.

03 plus 6.

56 divided by 0.

041 times 12.

And the question is why should Cala not round 0.

041 to 0.

And the answer is if you divide a number by zero, you get a math error.

So if you try it on your calculator, if you try this calculation, if you input it on the calculator and you round 0.

041 to the nearest integer, which would be zero, to nearest 10th, which would be zero, you get a math error.

So in this case, it would be better if Cala rounds this number to the nearest hundreds.

So that will be 0.

04.

Unless you can work out her calculation, which is then, which leads on to E, this question over here.

So if she rounds up 0.

041 to the nearest hundredth, then she can approximate the answer and get 40.

I'm going to read this page to you, and I want you to follow through what I am reading.

I mean, you're going to get a chance to work for the question.

An interesting number in maths is pi, which is approximately 3.

1415926535 and it goes on and on and on.

Now, they've given you 22 divided by seven is approximately 3.

142857143.

If I round both these numbers up to three decimal places, I would get 3.

142.

Your task now is to use the numbers zero to nine to try to find another fraction that when you round up would give you 3.

142.

So I want you to pause the video now and attempt this fine fractions that if you divide them to get together you would get a number that is rounded up to 3.

142 to three decimal place.

And if you're struggling, then you can carry on watching the video and I will provide you with some support as well.

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

Okay.

If you need some more support, this is the numbers that I've put in my fraction.

So I've got 355 divided by 130.

And if I type that on my calculator, I get 3.

14159292.

Run that up to three decimal place and I get 3.

142.

So this is one that I came up with using a lot of trial and error.

So you can do the same thing as well using some numbers between zero and nine.

We have now come to the end of this lesson.

Well done for sticking all the way through and completing the task.

Send your work to your teachers.

Let them see what you've done.

Show off how awesome you are, and I'll see you at the next lesson.

I've finished the video