Lesson video

Hi everyone, my name is Miss Coo, and I'm really excited to be learning with you today.

We'll be looking at one of my favourites.

We'll be looking at multiplicative relationships.

And it's one of my favourites because it appears so much in real life.

I really hope you enjoy the lesson today.

So let's make a start.

Hi everyone and welcome to this lesson on ordering numbers in standard form, and it's under the unit standard form.

And by the end of the lesson you'll be able to compare and order numbers written in a mixture of standard and non-standard and not quite standard form.

So key words, we'll be looking at standard form.

And standard form is when a number is written in the form A multiply by 10 to the power of N, where A is a number in between 1 and 10, including 1 but not including 10, and N is an integer.

Today's lesson will be broken into 2 parts.

First of all we'll be looking at comparing numbers in standard form and the second will be ordering numbers using standard form.

So let's have a look at comparing numbers in standard form.

Well we know standard form is the convention to write very large or very small numbers.

We use standard form in a number of different industries.

For example, technology, medicine or astronomy.

And having a convention to write very big numbers or very small numbers is important as is knowing how to use them and to recognise, size and order.

So what I'm gonna do, I'm gonna give you a short task.

Put these things in ascending order and then I want you to match with the approximate standard form measurement.

So what do you think in ascending order is the smallest to largest, the height of Mount Fuji, the height of the Gherkin, length of a football pitch, the height of the statue of Liberty or the latitude of the earth.

See if you can put them in ascending order and then match it with these approximate standard 4 measurements, 1.

1 times 10 squared metres, 1.

1 times ten to the 5 metres, 9.

3 times 10 metres, 1.

8 times 10 squared metres and 3.

8 times 10 to the 3 metres.

See if you can give it a go and press pause for more time Great work.

So let's have a look at how you've got on.

I'm going to put these objects or things in order first.

So in ascending order we have the statue of liberty is the smallest.

Then we had the length of a football pitch, the height of the Gherkin, the height of Mount Fuji, and then finally the latitude of the earth.

So now we have these objects in ascending order.

Let's match it with the approximate lengths.

Well, matching with the approximate lengths in standard form, the statute of liberty is 9.

3 times 10 metres.

The length of a football pitch is 1.

1 times 10 squared metres.

The height of the Gherkin is 1.

8 times 10 squared metres.

Mount Fuji is 3.

8 times 10 to the 3 metres.

And the latitude of the earth is 1.

1 times 10 to the 5 metres.

So removing the imagery, how do you identify that these standard forms are in ascending order? Well, you take a little look.

Well the exponents are in ascending order, so that's the main thing that you want to look at.

So you can see we have an exponent of 1, exponent of 2, exponent of 2, exponent of 3 and then exponent of 5.

But where the exponents are the same, we order the numbers.

So look at that 1.

1 and 1.

8.

So we've put these in ascending order when the exponents are the same.

Now ordering the exponents can also be seen using a place value chart.

The bigger the exponent, the larger the number.

For example, 9 times 10 to the 10 is bigger than 9 times 10 to the 6, and you can see that on our place value table.

I'm gonna do is give you a quick check.

Alex says he's put these in ascending order, smallest to largest.

So the smallest is at the very top and the largest is at the bottom.

Now I want you to find his error and explain why he's not put them correctly in ascending order.

See if you can give it a go and press pause for more time.

Well done.

Let's see how you got on.

Well, 2.

1 times 10 to the 5 is bigger than 2.

099 times 10 to the 5.

Converting 2.

1 times 10 to the 5 to an ordinary number, it's 210,000.

And converting 2.

099 times 10 to the 5 is 209,900.

Alternatively, you could have just looked at the actual numbers given that both of them have the same base of 10 and the same exponent of 5.

So 2.

1 is bigger than 2.

099, so therefore 2.

1 is larger.

Well done if you got this one right.

So now I want you to do another check.

Here I want you to put the following in ascending order, smallest to largest, for both A and B.

See if you can give it a go.

Press pause for more time.

Great work.

Let's see how you got on.

Well the smallest number should have been 3.

45 times 10 to the 3.

Look at that exponent.

The 3 was the smallest, followed by 2.

48 times 10 to the 4, then 2.

51 times 10 to the 4, then 9.

8 times 10 to the 5 and 1.

3 times 10 to the 9.

Really well done if you've got this one.

Next, let's have a look at B, in ascending order, let's look at those exponents first.

On 9.

2 times 10 to the 10 has the smallest exponent of 1.

Then we have 6.

798 times 10 squared, 6.

8 times 10 squared, 1.

389 times 10 to the 4, and 2.

1 times 10 to the 4.

Really well done if you got these ones right.

Now let's have a look at really small objects.

I want you to put these in descending order.

So from biggest to smallest, and then match with the approximate standard form.

So let's look at the items first.

We have the radius of an atom, the length of a strawberry, the width of a microchip, the thickness of a human hair and the width of a fingernail.

What I'd like you to do is put those objects in descending order.

And then I want you to see if you can match it to the approximate standard form.

Two times 10 to the negative 6 metres, 8 times 10 to the minus 5 metres, one times 10 to the minus 10 metres, 2.

5 times 10 to the minus 2 metres, 1.

5 times 10 to the minus 2 metres.

See we can match the approximate standard form with those objects.

See if you can give it a go.

Press pause for more time.

Great work.

Let's start with these objects first.

So putting our objects first, largest to smallest in descending order.

The largest would be the length of a strawberry, followed by the width of a fingernail.

Then the thickness of a human hair, followed by the width of a microchip and finally the radius of an atom.

Great work if you got those.

Well, matching with the approximate standard form lengths, we have 2.

5 times 10 to the minus 2 metres, 1.

5 times 10 to the minus 2 metres, 8 times 10 to the minus 5 metres, 2 times 10 to the minus 6 metres and 1 times 10 to the minus 10 metres.

Really well done if you got this one right.

So I'm going to remove that imagery now and what I'd like you to do is identify how did you know these standard forms were in descending order? Have a little think.

Well, we are looking at the exponents again.

So if the exponents are in descending order, then that really does help us put it in order.

So we have minus 2, minus 5, minus 6 and minus 10.

So these exponents really do help us put our numbers in descending order.

But you might notice we have two standard forms where the exponents are the same.

So in that case that means we order the value or the number of A.

So if you look at the 2.

5, and the 1.

5, we're ordering these in descending order.

2.

5 is greater than 1.

5.

Well done.

So ordering using exponents can also be seen using the place value chart.

The bigger the exponents, the larger the number.

So let's have a look at 2 multiply by 10 to the minus 5.

Well, I've put this on my place value chart so you can see it here.

And this is obviously greater than 2 times 10 to the negative 9 which I've put in my place value chart as well.

So using a place value chart, it really does help you visualise the size or the magnitude of our number.

Well done.

So now what I want you to do is put the following in ascending order.

So remember that smallest to largest.

See if you can do it for A and B.

Give it a go and press pause if you need more time.

Well done.

Let's see how you got on.

Well let's look at those exponents first.

So remember, smallest to largest.

What is that smallest exponent? Well our smallest exponent is negative 4, but we have 2 numbers with an exponent negative 4.

So which is smallest? Well it's the 4.

4 times 10 to the negative 4.

So 4.

4 times 10 to the negative 4 is our smallest number.

Well done.

Now the next smallest number is 4.

6 times 10 to the negative 4.

4.

6 is bigger than 4.

4, so that's why it comes second.

Next, looking at our next smallest exponent, it's negative 2, so it's 5.

6 times 10 to the negative 2.

Then we have 1.

2 times 10 to the negative 1, and then 1 times 10 to the 10.

Well done.

For B, let's have a look at those exponents again.

Smallest to largest, which is our smallest exponent? Well we have 2 numbers with a negative 6 exponent, which is the smallest, well the smallest would be 6.

798 times 10 to the minus 6.

Well done if you've got this.

Followed by 6.

9 times 10 to the minus 6.

Then from here, 6.

45 times 10, 6.

1 times 10 to the 6 and then 6.

798 times 10 to the 6.

Great work if you got this one right.

Now what we're going to do is another check question.

Aisha says she cannot put these in ascending order because then not in standard form.

Explain why she can put them in order and then I want you to order these numbers in the form they are given.

See if you can give it some thought and then give it a go.

Press pause for more time.

Aisha can convert them all to standard form and then order or alternatively she can convert them to an ordinary number and then order.

But what is important is to recognise the working out will help us order what was originally given in the question.

So you should always order what was given in the question and not your working out.

So let's do some working out first.

So for my working out, I'm gonna convert them all standard form.

So that means 0.

00439, 4.

39 times 10 to the negative 3.

This is already in standard form 'cause you don't have to do anything here.

This in standard form is 9.

2 times 10 to the minus 1.

24,000 in standard form is 2.

4 times 10 to the 4 and this is already in standard form so we don't have to do anything here.

Now from here I'm going to order what was originally given in the question.

So what's the smallest? Let's have a look at our working out.

Well the smallest would be our 4.

1 times 10 to the negative 4.

So going back to the original question, that means we are ordering 4.

1 times 10 to the negative 4.

That's my smallest.

The next smallest would be 4.

3 times 10 to the negative 3.

But remember the question gave us 0.

00439 so that's why I have to order.

Then we've got 9.

2 times 10 to the negative 1, but the question originally gave me not 0.

92.

So that's what I have to order.

Next, the next smallest is 2.

3 times 10 to the 4.

Then finally followed by 2.

3 times 10 to the 4 and then 24,000.

Really well done if you've got these right.

Now it's time for your task.

What I want you to do is put the following in ascending order, smallest to largest.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question two.

Question two, put the following in ascending order in the format they are given.

See if you can give it a go.

Press pause for more time.

Great work.

So let's move on to question three.

Question three says, I've put the following in ascending order by ordering the exponent first and where the exponents are the same have ordered the number.

Explain why Laura has not correctly ordered these numbers.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to these answers.

Well, I'm gonna put all these numbers in ascending order, press pause to mark them if you need more time.

Well done.

Question two, I'm going to do a little bit of working out and convert them into standard form, but remember we're ordering what the question originally gave us.

So the answer would be here, 8.

2 times 10 to the negative 4, 0.

0089, 0.

1, 1 times 10 to 3 and 90,000.

Great work if you've got this one right.

For B, here is the original question and this is my working out.

I've converted them to standard form so I can order, but remember order what the question gave.

So here are my answers, which is originally the format given in the question.

Well done if you've got this.

Press pause if you need.

For question three, can you explain why Laura has not correctly ordered the numbers? Well to order according to the exponents and then the A number, all the numbers must be correctly written in standard form first.

Some of these numbers are not in standard form, so that means she wasn't able to order successfully.

Great work everybody.

So let's move on to the second part of our lesson, which is ordering numbers using standard form.

Now standard form allows a standard convention of writing very big or very small numbers.

And if it wasn't for standard form there would be too many different representations for the same number.

For example, all of these representations represent 53 and we don't want that.

We wanna come up with a standard approach to represent the number 53.

So working out the original number using skills and multiplication of fractions, the associative law and or multiplication of decimals allows us to write it correctly and in standard form.

And then from there we can order if needed.

For example, how would you work out the number 45 multiply by 10 cubed? Well there are lots of ways in which you could do it.

You could do it in steps.

45 multiply by 10, multiply by 10, multiply by 10, which is 450 times 10 times 10, which is 4,500 multiplied by 10, which is then 45,000.

So you could do it in steps.

In standard form then the answer would be 4.

5 times 10 to the 4.

So we successfully written 45 times 10 to 3, which is not in standard form in standard form by using these little steps.

We can also do the same for this.

Imagine if you had 469 times 0.

001.

Well we know that's the same as 469 times not 0.

1, times not 0.

1 times 0.

1.

Doing it in steps, this is the same as 46.

9 times 0.

1 times 0.

1.

Doing it in again and another step, this is the same as 4.

69 times 0.

1, which is then the same as 0.

469.

And I can write this in standard form now, 4.

69 times 10 to the negative 1.

So all we've done now is write a calculation in standard form using these little steps.

Now what I want you to do is I want you to think about what number is represented by all these calculations, for A and B.

And for C, I want you to identify which calculation is the odd one out and I want you to explain.

See if you can give it a go.

Press pause if you need more time.

Great work.

So let's identify these answers.

Well for A, it's 0.

92.

For B, it's 4.

5.

And for C, well all of the other answers equate for 8,200 except for this one.

So well done if you've got this.

Now I'm gonna do is a quick check.

I'll do the first part and I want you to do the second part.

Using correct standard form, we're asked to put these numbers in ascending order, smallest to largest.

So I'm gonna have a look at 54 times 10 squared.

First of all, I'm gonna work this out because it's not in standard form.

Well this is the same as 54 times 10 times 10, which is 5,400, and now I've correctly written it in standard form, 5.

4 times 10 to 3.

Let's look at 653 times 1 over 10 squared.

Well, this means 653 times a 10th and times another 10th, which is the same as 6.

53, which is the same in standard form as 6.

53 times 10 to the power of zero.

Next 8.

9 times 10.

This is nice because it's in standard form.

9,900 times 0.

01.

Well, working this out it's the same as 9,900 times 0.

1 times 0.

1, which is 99.

And I can write 99 in standard form as 9.

9 times 10.

So from here I can now successfully order.

Looking at those exponents, what's the smallest one? Well it's gonna be my 6.

53 times 10 to the zero.

Zero is the smallest exponent.

Then the next smallest exponent is the 1.

So I have 2 numbers which have an exponent of 1, 8.

9 times 10 and 9.

9 times 10.

So which is the smallest? What's 8.

9 times 10? So 9.

9 times 10, which is our 9,900 times 0.

1 is our next value, finally followed by 54 times 10 squared.

Remember to order what was given in the original question.

Well done if you got this.

Now what I want you to do is try your own check question Using correct standard form, put these numbers in ascending order, smallest to largest.

See if you can give it a go.

Press pause if you need more time.

Great work.

Let's see how you got on.

Well 1.

2 times 1 over 10 is the same as 1.

2 times 10 to the minus 1.

8.

9 times 0.

001 can be written as 8.

9 times 10 to the minus 3.

9.

8 times 1 over 10 squared is 9.

8 times 10 to the minus 2.

And 7.

8 times 10 squared, great, I don't have to do anything here.

It's 7.

8 times 10 squared.

So looking at this working out, let's put them in ascending order while the smallest exponent would be that negative 3.

So that means 8.

9 times percent of the minus 3, which is our 8.

9 times 0.

001 is our smallest, followed by our 9.

8 times 1 over 10 squared and our 1.

2 times 1 over 10 and finally are 7.

8 times 10 squared.

Well done if you got that one.

Excellent work everybody.

So let's have a look at another check question.

Jun and Andeep put these calculations in ascending order but they both got the same answer.

But are they correct? And I want you to explain their different methods.

See if you can give it a go.

Press pause for more time.

Well done.

Let's see how you got on.

Well both are correct.

Jun has decided to convert the numbers to standard form and then order.

But Andeep has decided he wanted to convert to an ordinary number and then order.

Both of their methods are absolutely fine, which explains why they got the same correct answer.

However, I want you to have a look at this.

Here are some calculations given to Andeep to put in ascending order.

Now Andeep wants to write them all as an ordinary number first, just like he did before; and then order.

Can you explain if this approach is appropriate? See if you can give it a go.

Press pause for more time.

While the numbers are so small there will be too many zeroes which can increase the likelihood of errors.

So converting to standard form and then ordering would be more efficient.

Well done if you got this.

Excellent work everybody.

So now it's time for your task.

For question one, sing inequalities, less than, greater than or equal to compare the sizes of each number and ensure you show your working out.

See if you can give it a go.

Press pause for more time.

Great work.

Let's move on to question two.

Question two, by working out the number, write in standard form and order the original form given in the question.

See if you can give it a go.

Press pause for more time.

Well done.

Let's move on to these answers.

Fill for question one, we should have got 38 times no 0.

01, it's greater than 4.

8 times 10 to the negative 2.

I've written them both in standard form so you can see.

B, we've got 780,000 multiply by 0.

001 is less than 99 times 10 squared.

Writing it in standard form, you can see why.

For C, 139 times 1 over 10 squared is greater than 4,820 times 1 over 10 to the 4.

Writing it in standard form, we have this so you can see why it is greater.

For D, 1600 times 10 squared is equal to 160,000 times 10 to the 4.

And I've done this working out here.

Great work if you've got this one right.

For question two, by working out the number, write in standard form and order the original form given in the question.

I've written my following in standard form and then I've ordered them accordingly.

Great work if you've got this one right.

For question two, same again, I've written it in standard form and then from here I've ordered them accordingly.

Amazing work if you've got this one right.

Lastly for question two, writing them in standard form I have this and then here I've just simply put them in ascending order.

Amazing work if you've got these ones right.

Excellent, everybody.

So in summary, we know standard form is the convention to write very large or very small numbers.

And we use standard form in a number of industries.

Once numbers are written in standard form, we can order using the exponents.

The bigger the exponents, the larger the number.

For example, 9 times 10 to the 10 is greater than 9 times 10 to the 6, or 2 times 10 to the negative 5 is greater than 2 times 10 to the negative 9.

And converting all calculations to standard form or sometimes to an ordinary number allows ordering to be more efficient.

Great work, everybody.

It was wonderful working with you.