Lesson video

Hello, and welcome to this lesson on sorting large numbers with me, Miss Oreyomi.

For today's lesson, you'll be needing your paper and your pen or something you can write on and with.

It would also help if you minimise the distraction by putting your phone on silence, the duration of the lesson, or also trying to get into a space with less noise or distractions.

So if you need to do those things now, please do them and then press play to resume the video when you're ready.

Okay, for your try this task, you are to sort these from the smallest number to the greatest number.

So I've got this in another format for you.

Like so, try to sort these numbers from the smallest numbers to the greatest numbers.

So pause your screen, attempt this task and then when you're done, press resume to carry on with the lesson.

Okay, hands up if you're actually able to sort this out from smallest to greatest.

Hands up, if you thought, okay, this is too hard, I'm just going to resume the lesson and hope the teacher gives me the answer.

Probably a lot of you, 'cause this was meant to actually confuse you, confession time.

Because when you see numbers like this scattered all around the page and you've got large numbers everywhere.

It can be really hard to know which one is the smallest, which one is the largest.

Why are there so many zeros staring at me? We write numbers like this, large numbers like this in standard form, because they help us to sort numbers easier.

They help us to see which one is larger than which when we're writing an ordinary number in standard form, and over here are ordinary numbers.

When we're writing ordinary numbers in standard form it's split into two.

So our first part of our standard form is usually a number between one and 10 and that number can be one itself.

So it's a number that is one and is less than 10.

And then the second part is always raised to a power of 10.

It's always raised to a power of 10.

So I've got 28,000, if I want to write 28,000 in standard form, the first part of my number has got to be between one and 10, and for that to be between one and 10, I'm going to put a decimal point between my two and my eight.

2.

8 is a number between one and 10.

Now I'm thinking I am raising this to a power of 10, what should I raise this to that if I multiply it by 2.

8 would give me my value of 28,000? I hope you've said four because 10 to the power of four is the same as writing 10 times, 10 times, 10 times 10, which is the same as 10,000.

So 2.

8 times 10,000, if you remember from previous lessons is 28,000.

So 28,000 written in standard form is 2.

8 times 10 to the power four.

Let's look at our second example.

I've got.

I need to write this number in standard form, so I need a number that is between one and 10.

Well, the only non zero number here's is a four.

So I'm going to write four there.

Now, what power of 10 should I raise it to? I'm going to count from where I've put my decimal point, so I put my decimal point here, so it's going to be one, two, three, four, five, six, seven, eight, nine, 10.

So it's going to be four times 10 raised to the power of 10.

Let's look at a second one there, a third one rather.

So I want a number between one and 10.

Where would I put my decimal point so that my number is between one and 10? Well, is going to be between this one and the zero, isn't it? So I'm going to write, 1.

05, 'cause those are my significant numbers.

So I've put 1.

05, and I need to raise it to a power of 10.

If I put my decimal point here, I'm going to count one, two, three, four, five, six, seven, eight.

And that is times 10 to the power of eight.

So the first part of my number is always a number between one and 10.

And the second part of my number is always raised to the power of 10.

So I'm going to put the rest up for you.

Now, when you see this, do you see how much easier it is for you to sort these number? Looking at your screen, what is the largest number? It would be this one, wouldn't it? Because it's got the largest power raised to the power of 20.

What is the smallest number on your screen? It'll be our 28,000 because it is raised to a power of four.

So writing large numbers in standard form really helps us to visualise and therefore to sort numbers out easier.

So we've looked at how to convert ordinary number to standard form.

What if they've given us the standard form and they want us to convert it to an ordinary number.

I would multiply out, I'll actually do the calculation.

So I know from previous lesson that I've got 1.

2 and 10 squared.

I know that 10 squared is a hundred, therefore, it is the same as writing 1.

2 times 100, which is 120.

So I've gone from standard form here with a base raised to a power.

Raised power of 10 and multiplying out to get an ordinary number of 120.

Here, I've got three times 10 to the power four, again, I know that ten to the power four is 10,000.

So three times 10,000 is 30,000.

Okay, I've got 3.

141592, your brain is going, that's PI, times 10 to the power of three.

Well, if I'm multiply this by a thousand, remembering that I'm moving my numbers to the left three times.

So I would have 3141.

592.

So one, two, three, and this would be my number as this would be converting 3.

141592 times ten to power of three, to an ordinary number would be this right here.

Okay, your turn then, if I have 79,000 and then the rest of the numbers, Can you write it in standard form? And then can you move on to the other side and write each of the following as an ordinary number? Okay, hopefully you had a go at this.

I've got this number here and I know that my base must be a number between one and 10.

So I'm going to put my decimal point there, it would be 7.

9 and then to get to the end, I have to move one, two, three, four.

So it'd be 7.

9 times 10 to the four.

For this one my decimal point is going to be between the three and the one, because that is a number that is between one and 10.

So it's going to be 3.

1 times one, two, three, four, again, times 10 to the four.

Next one then, I'm going to put my decimal points between 3.

345.

Okay, so if you see I'm taking all the significant numbers, so to speak.

So three, three, four, five, I'm taking all the non zero digits.

So I've put my decimal point there, how many times do I have to move, before I get to the end? It's one, two, three, four, five.

So it's going to be 3.

345, times 10 to the five.

Now I want to write this as an ordinary number.

Say here, I am multiplying 1.

37 times 10,000.

So I am going one, two, three, then zero, zero, and that would be my final answer.

This one, it's going to be three and 10 zeros.

One, two, three, four, five, six, seven, eight, nine, 10.

So three times 10 to the raise of power 10 will be written as this as an ordinary number.

Let's look at C then, I've got 9.

979, and I am multiply that by 10 to the seven.

So I'm going one, two, three, four, five, six, seven.

So I'm going to put my placeholders here and remove that decimal point over here, and this is my final answer.

So check in your work and ensuring that you got those.

So to write it in standard form, you've got a base between one and 10 and is raised to the power of 10.

And to write it as an ordinary number, you're carrying out the calculation you're given.

It is now time for your independent task.

So I want you to pause the video now, attempt every question on your worksheet and then return, and we'll go.

Press play to return, and we'll go over the answers together.

So pause the video now and attempt the independent task.

Okay, hopefully you had a go at that and hopefully you are able to use the learning from the lesson to attempt every question.

So this, I want to write this in standard form.

Like I said, my base must be a number between one and 10.

In this case, it will be 2.

9.

So I've got 2.

9 times one, two, three, 10 to the power of three.

Here, it'll be eight times 10 squared.

Here, it'll be 2.

2, so here's one, two, three, four, five, six, seven, times 10 to the power of seven.

Here, we're going to have 6.

7 times 10 to the power four.

Over here, we're going have 8.

7005 then I'm going to have one, two, three, four, five, six, seven, eight, nine, times 10 to the power of nine.

Over here, we're going to have 4.

4471.

Okay, so this is a number between one and 10 and from my decimal point all the way to the end of my number, it's one, two, three, four, five, six, seven, eight.

So it's times 10 to the power of eight.

Lastly, on this page, we'll have 9.

04 and it's one, two, three, four, five, times 10 to the five.

How did you get on? Did you get everything correct? So check in your answers for number two.

You may need to pause the video if you need longer to go over it, and your answers for three, four, and five.

How did you get on? Okay, for your explore task for each set.

So set one, set two and set three.

So we've got one here, two here and three here.

For each set, find the odd one out? So which number in your set is the odd one out? And write the correct standard form? So for example, 30.

3, we know, that is not the correct sign of the form because the base is not between one and 10.

Here, the base is also not between one and 10.

So for each set, look at each one, what's the odd one out? And for each one where the base is not between one and 10, for each one way, it's not written in standard form.

Write the correct standard form.

So pause your screen now and have a go at that and see how you get on with that.

Really good job for sticking all the way through and completing your work and working hard on the questions.

Make sure you complete the quiz before you go, just to consolidate your knowledge and see what you've learned from today's lesson.

And I will see you at the next lesson, bye.