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You can describe numbers and sizes of cells using appropriate units and standard form.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Most animals and plants are made up of millions or billions of cells.
Cell numbers can be expressed in standard form.
Cells are usually too small to see with the unaided eye.
Comparison of sizes of eukaryotic and prokaryotic cells, and cell structures, in µm, nm, and in metres in standard form.

Common misconception

Pupils commonly convert units incorrectly, multiplying when they should divide or dividing when they should multiply.

It can help to relate the unit conversions in the lesson to an everyday example, e.g. pounds to pence.

Keywords

Million - 1 000 000, or one thousand thousand, or 10⁶.
Billion - 1 000 000 000 or one thousand million, or 10⁹.
Standard form - A way of writing down very large or very small numbers easily; e.g. 1000 = 10³.
Micrometre (µm) - One millionth of a metre, or 1 m / 1 000 000, or 1 × 10⁻⁶ m.
Magnification - Making small objects appear larger in order to see more detail.

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Hi, I'm Mrs. Hudson, and today I'm going to be teaching you a lesson called The Size and Scale of Cells, Including Standard Form.

This is a biology lesson and it comes under the unit titled Eukaryotic and Prokaryotic Cells.

The outcome of today's lesson is I can describe numbers and sizes of cells using appropriate units.

There will be some really important words that we'll use in today's lesson, and those keywords are million, billion, standard form, micrometre, and magnification.

Let's have a look at what those words mean.

A million, if you are going to write it as a number, is a one followed by six zeros, or you could say it's 1,000 thousand and written in standard form, it's 10 to the power of six.

A billion, written as a number, is one followed by nine zeros or 1,000 million, and written as standard form 10 to the power of nine.

Standard form is a way of writing down a very large or very small number easily.

For example, 1,000 written a standard form is 10 to the power of three.

Micrometre is millionth of a metre or one metre divided by one million, or written a standard form, one to the power of 10 to the minus six metres.

Magnification is making small objects appear larger in order to see in more detail.

If you want to pause the video now to make a note of those keywords, please do, and then press play when you're ready for me to carry on with the rest of the lesson.

Today's lesson is going to be split up into three different parts.

In the first part of the lesson, we're going to be looking at units of microscopy.

Then we're going to move on to comparing sizes, and then in the final part of the lesson we're going to be doing some microscopy calculations.

Let's get going with the first part though, looking at units of microscopy.

Most cells are too small to see with the unaided eye.

To observe cells in detail, a microscope is necessary.

We use micrometres, which has a symbol of funny little um, and nanometers with the symbol nm when measuring cells and subcellular structures.

So for us to be able to see microscopic cells, we have to use a microscope, and we can see here there's a picture of some E.

coli.

Each individual rod shape is one E.

coli organism, and if you look carefully at this picture, you can see that it says one micrometre on there with a scale bar and it's just circled there.

So we're measuring the E.

coli in micrometres.

Why might it be better to use nano metres rather than micrometres to measure subcellular structures such as ribosomes? Well, we can see on this diagram that one E.

coli doesn't measure that much bigger than one micrometre, and a ribosome is much smaller in size than an E.

Coli, so therefore we have to use nanometers because they're a more appropriate measurement.

In fact, one ribosome measures roughly between 20 to 30 nanometers in size.

That would be 20,000 to 30,000 micrometres.

When working with very small or very big numbers, we use something called standard form.

Standard form numbers are written as A times by 10 to the power of n, where A is a number greater than one, but less than 10, and n is the power of 10.

So n is how many times you've multiplied or divided that number by 10.

One of the bacteria in this image is 2.

6 micrometres in length.

6 micrometres is the same as writing 0.

0026 millimetres.

6 micrometres is also the same as 2,600 nanometers.

We can write these using standard form.

So 0.

0026 written as standard form is 2.

6 times by 10 to the minus three millimetres.

Now the minus three after the 10 just means that we have divided 2.

6 by ten three times.

So effectively we've divided 2.

6 by 1,000.

2,600 written in standard form is 2.

6 times 10 to the power of three nanometers.

Now again, 10 to the power of three just means that we're multiplying 2.

6 by ten three times.

So effectively we're times it by 1,000.

So what we can work out from this is that if something has a negative to the power integer, it's probably going to be a small number, whereas if something has a positive power integer, it's probably going to be a bigger number.

Let's look at some units used in microscopy in a little bit more detail.

So the units we've got here are metres, millimetres, micrometres, and nanometers.

Make sure that you familiarise yourselves with the correct symbols for those units.

Now, relationships to other units, let's look at a metre to begin with.

There are 1,000 metres in a kilometre.

So one metre is one 1,000th of a kilometre.

Division of a metre into standard form, so if we're going to represent a metre in metres in standard form, it'll be one times by 10 to the power of zero because anything to the power of zero is one and there is one metre in a metre.

Let's look at millimetres now.

There are 1,000 millimetres in a metre, so one millimetre is one 1,000th of a metre.

If we wanted to represent a millimetre in standard form in comparison to a metre, it would be one times by 10 to the minus three, and this is because we've divided one by ten three times.

We've divided one by 1,000.

Micrometres, there are a million micrometres in a metre, so one micrometre is one 1,000th of a millimetre.

To write one micrometre in comparison to a metre in standard form, you'll be one times by 10 to the minus six.

We've divided one by ten six times, and then the nanometers, there are one billion nanometers in a metre and a nanometer is one 1,000th of a micrometre.

So to write a nanometer in standard form in comparison to a metre, it'll be one times by 10 to the minus nine because we've divided one by ten nine times.

Let's do our first check for understanding.

What is the correct unit for a micrometre, A, B, C, or D? This is D, it's that funny looking U with an M.

Well done if you got that right.

Next question, starting with the largest, sort the units of measurement into decreasing size order, A, micrometre, B, metre, C, millimetre, D, nanometer.

Remember you're starting with the largest.

So this should be B, metre, first, then C, millimetre, then A, micrometre, and then finally D, nanometer.

And the last question, which of the following are correct, A, 1,000 equals one times by 10 to the power of three, B, 0.

066 is equal to 6.

6 times by 10 to the minus two, C, 476,000 is equal to 4.

76 times 10 to the minus five, and D, 0.

000054 is equal to 5.

4 times 10 to the minus five.

Let's see if we got that right.

So A is correct, B is also correct, and D is also correct.

C is incorrect because you can see that there's a negative power there.

So that would mean that the number is much smaller.

Actually that is 4.

7, six times 10 to the positive five.

Well done if you recognised that wasn't right.

Now that we can recognise units, let's have a look at how we convert between them.

So here we've got metres, millimetres, micrometres and nanometers, and then we've also got what they would be written as a standard form if we were talking about one in comparison to a metre.

So if I wanted to convert between metres and millimetres, I would times by 1,000 and this is because there are 1,000 millimetres in a metre.

If I wanted to convert from millimetres to micrometres, I would multiply by 1,000 and again, from micrometres to nanometers I would multiply by 1,000 again.

However, if I wanted to convert from nanometers to micrometres, rather than times by 1,000, I would divide by 1,000, and then converting from micrometres to millimetres, I would divide by 1,000, and converting millimetres to metres, I would divide by 1,000 again.

We will need to use some of these unit conversions later in the lesson, so I would recommend to pause the video and make a note of these conversions now.

So let's have a look at some conversions.

An amoeba has a diameter of 90 micrometres.

What is its diameter in nanometers and what is its diameter in millimetres? So we need to do some conversions.

Well, 90 micrometres in nanometers, we're going to times by 1,000 to get 90,000 nanometers.

Let's write this number now in standard form.

90,000 is the same as saying nine times by 10 to the power of four.

We have timed nine by 10, four times.

Let's look now at the diameter in millimetres.

So 90 micrometres in millimetres, we have to divide 1,000 to get 0.

09 millimetres.

Let's write that number now in standard form, nine times by 10 to the minus two is the same as 0.

09 millimetres.

So we have divided nine by 10, two times.

Your turn to have to go at something similar now.

And E.

coli bacterium has a diameter of 2.

2 micrometres.

What is its diameter in nanometers, and then write that number in standard form, and what is its diameter in millimetres, and write that number in standard form.

See if you can have a go now.

So 2.

2 micrometres, we have to times by 1,000 to get 2,200 nanometers.

And then writing that in standard form, we should have 2.

2 times by 10 to the power of three nanometers.

And what is a diameter in millimetres? We would do 2.

2 divided by 1,000 to get 0.

0022 millimetres, and then to convert that into standard form, it would be 2.

2 times by 10 to the minus three.

Really good job if you managed to get both of those right, well done.

We should be ready now to move on to the first task of the lesson.

So in the first part of the task, you need to convert the following to complete the table using standard form.

So the headings of the table are metre, millimetre, micrometre and nanometer, and you've been given a number in each row.

You have to convert those numbers into the correct unit in standard form.

Then for question two, a human egg cell has a diameter of 118 micrometres.

What is its diameter in nanometers? What is its diameter in millimetres? And give your answers in standard form.

And then finally for number three, and adult fruit fly has a length of three millimetres.

What is its length in nanometers? What is its length in micrometres? Give your answer in standard form.

I'm sure you're gonna do a great job.

Pause the video now and then press play, ready for me to go through the answers.

Let's see how we did.

So starting with 2.

8 times 10 to the minus one, if we wanted to convert the metres into millimetres, we would have to times by 1,000, and written a standard form that would be 2.

8 times 10 to the power of two.

Then we were times by 1,000 again to get to micrometres, which gives us 2.

8 times 10 to the power of five, and then times by 1,000 again to get to nanometers, 2.

8 times 10 to the power of eight.

Now looking at the next one, 6.

4 times 10 to the power of zero millimetres.

So to get to metres it's going to be 6.

4 times by 10 to the minus three.

We've divided by 1,000.

Then to convert to micrometres we times by 1,000.

So it's 6.

4 times 10 to the power of three, and nanometers, 6.

4 times 10 to the power of six because we've multiplied by 1,000 again.

Now looking at our micrometres, 1.

5 times 10 to the power of one, to work out our metres, it's going to be 1.

5 times by 10 to the minus five, in millimetres, 1.

5 times 10 to the minus two, and then we multiply by 1,000 to get nanometers, 1.

5 times by 10 to the power of four.

Brilliant job if you manage to get all of those correct.

So for question two, 118 micrometres is the same as 118,000 nanometers we've multiplied by 1,000.

Written in standard form, this would be 1.

18 times by 10 to the power of five nanometers.

To put this into millimetres, we would have to divide by 1,000, which would give us 0.

118 millimetres and written in standard form, this is 1.

18 times 10 to the minus one millimetres.

And for number three, three millimetres is the same as writing three million nanometers and that written in standard form is three times by 10 to the power of six.

If we wanted to write this as micrometres, we would times by 1,000, which would give us 3,000, and as standard form that would be written as three times by 10 to the power of three micrometres.

Really good job if you managed to get all of those right.

Pause the video if you need to correct anything, but then press play when you are ready for me to go through the rest of the lesson.

Great job so far, well done.

Now we know our units of microscopy, let's have a look at comparing some sizes.

Most plants and animals are multicellular and are made up of millions or billions of cells.

Those that are unicellular, which means they consist of only one cell, are microscopic, and that means that we would need a microscope to be able to view them.

And we can look at this diagram here, which is a sliding scale of different sizes and at the very left you've got really small measurements, so 0.

1 nanometer, and then gradually they get bigger, so we go to micrometres, then millimetres, centimetres, and then finally measuring organisms in metres such as humans and the blue whale.

Let's look at some specific organisms on this scale.

So viruses are between 10 nanometers and 100 nanometers in size, but viruses are not considered to be living things.

We can see we've got some bacteria, prokaryotes, and these are unicellular organisms, so they're made up of just one cell, and their sizes are varied between one micrometre to 10 micrometres.

And then we've got some eukaryotic cells, which can be unicellular organisms such as protists, or they can be multicellular organisms, but their sizes are slightly larger and they vary.

The sizes of living things on earth can be compared, but the organisms here between one nanometer up towards 100 micrometres, are all microscopic cells.

We would need to use a microscope in order to be able to see them.

Whereas if you go from the frog egg upwards, then these are much larger and will be visible with the human eye.

We can see how the different units of measurements are used on this scale.

So nanometers, the very smallest measurement is on the very left hand side, and micrometres is where we start to look at individual subcellular structures such as chloroplasts or prokaryotes like bacteria, and then small unicellular eukaryotic cells or individual cells in the human body.

Then we go into millimetres, so for example, a frog egg, centimetres might measure smaller eukaryotes like ants.

And then finally we start to look at metres when we measure larger eukaryotic organisms. Let's quickly check our understanding.

How many cells make up a unicellular organism, A, one, B, thousands, C, millions or D, billions? This is A, one, unicellular organisms are made up of only one cell.

Let's have a look now at comparing some sizes of organisms. So we've got an ant, amoeba, red blood cell, bacteria and virus, and all of them have got slightly different length or diameters.

You can see here that the length of an amoeba is 10 times the diameter of a red blood cell and we know that because the length of the amoeba is 90 micrometres, and if we divide it by the diameter of the red blood cell, nine, we get an answer of 10.

So the amoeba is 10 times the diameter of the red blood cell.

This is relatively easy for us to do because the amoeba and the red blood cell both have their length and diameter measured in micrometres.

When comparing size, it is important work in the same units.

It would be very difficult for us on this slide to compare the length of the ant and the amoeba because their lengths are written in different units.

Let's have a go at comparing some sizes.

So what is the length of the ant compared to the length of the amoeba? So here we have got the different units that I just said.

The ant's length is nine millimetres and the amoeba's length is nine micrometres.

Now for us to be able to compare them, we have to make sure that we've both got the same units.

So the first thing we need to do is convert the nine millimetres into micrometres, millimetres to micrometres we times by 1,000.

So nine times by 1,000 is 9,000 micrometres.

Now both of our organisms have lengths in micrometres, so we can compare them.

We divide the larger length, which in this case is the ants at 9,000 micrometres, by the smaller length which is 90, and we can work that out, which is 100, and say the ant is 100 times longer than the amoeba.

So it's really important when comparing sizes to make sure that the units are the same in order for us to accurately compare.

Your turn to have a go now.

So what is the length of the bacterium compared to the diameter of the virus? The bacterium has a length of one micrometre and the virus has a diameter of 100 nanometers, so you need to make sure they're in the same unit and compare them, have a go.

Well, first thing we need to do is convert micrometres to nanometers, so we times by 1,000, therefore the bacterium has a length of 1,000 nanometers.

We look then which is bigger, that's the bacterium.

So we divide 1,000 by 100 and the bacterium therefore is 10 times longer than the diameter of the virus.

Well done if you manage to get that right.

We're now ready to move on to the second task in our lesson.

You've been given three questions where you've got two different cells and you have to compare their sizes.

I'm sure you're gonna do a fantastic job.

Press pause and then play when you're ready for me to go through the answers.

Let's have a look at how we did.

So in the first example, we don't need to change any units because they're both in micrometres, but the egg cell is larger, so we divide 120 by 1.

5, and the egg cell is 80 times larger.

The second example, again, we've got the same units, we don't need to convert, but we would do 70 micrometres divided by 0.

35 to show that the palisade cell is 200 times larger.

And then in the final example, we've got 475 micrometres and seven micrometres.

So again, we don't need to do any conversions, but we do 475 divided by nine, which gives us 52.

78 times larger.

That's to two decimal places.

So if you've written it to one decimal place, you might have an answer of 52.

Brilliant job if you manage to get those right.

We're now ready to start the final part of our lesson, which is microscopy calculations, let's get going.

Magnification is a measurement of how many times an object has been enlarged.

We can calculate magnification using the real size and the image size of a magnified image using the following equation.

Magnification equals size of the image divided by the size of the real object.

We can rearrange the magnification equation to calculate the size of an image or the size of a real object.

And those rearrangements look like this.

Size of image equals magnification times by size of real object and size of the real object equals size of the image divided by size of a magnification.

I would recommend now that you write down these different rearrangements of the equation to help us for later questions in the lesson.

Let's have a look at some examples.

So calculate the magnification of an amoeba with a diameter of 90 micrometres in an image measuring 18 millimetres.

So here the diameter, which is the real size, is 90 micrometres and the image size is 18 millimetres.

Now the first thing we need to do is make sure that the units we are working with are the same, which they're not in this case.

So we need to convert 18 millimetres into micrometres, which you can look at below the picture of the amoeba, we've got 18 millimetres equals 18,000 micrometres.

Then we just have to put those values into our equation.

So magnification equals image divided by real size, the image size is 18,000 micrometres, and the real size is 90 micrometres.

So I do 18,000 divided by 90 gives me a magnification of 200.

Now just to recap, the most important part here is to check that the units are the same, and if not, you will need to convert them before you can put those numbers into the equation.

Your turn to have a go now.

Calculate the magnification of an E.

coli cell with a length of 1.

7 micrometres in an image measuring 10.

2 millimetres.

The equation's been written there for you, but before we put the values into the equation, please can you convert the image size into micrometres? So 10.

2 millimetres times by 1,000 gives us 10,200 micrometres.

Now use those values to work out the magnification.

So what we should have here is 10,200 divided by 1.

7 gives us a magnification of 6,000 times.

Well done if you got that right.

A look at another example, calculate the real size of a mitochondrion when the image size is 0.

3 centimetres and it is magnified 5,000 times.

Give your answer in millimetres using standard form.

So here we need to calculate the real size and we've been given the image size and the magnification.

We've got to give our answer in millimetres though and in standard form.

So the first thing we need to do is convert 0.

3 centimetres into millimetres because they've told us we need to give our answer in millimetres.

So 0.

3 centimetres is the same as three millimetres.

Now we're going to use the equation real size equals image size divided by magnification.

The image size is three, so we're going to divide it by 5,000, which is the magnification, and that gives us an answer of 0.

0006.

And that is the same as writing six times by 10 to the minus four millimetres.

And now let's convert our answer into micrometres.

So to get from millimetres to micrometres, we have to times by 1,000.

So six times by 10 to the minus four times by 1,000 is 0.

6 micrometres.

your turn to have a go now.

Calculate the real size of a coronavirus when the image size is 8.

4 times 10 to the minus two centimetres and it's magnified 7,000 times.

Give your answer a millimetres using standard form.

So use the same method as before to convert centimetres to millimetres and then put those values into the equation and write your answer in standard form.

Have a go now.

So the first thing we needed to do was convert 8.

4 times 10 to the minus two centimetres into millimetres, so we have to times it by 10, which gives us 0.

84 millimetres.

Then we use the equation real equals image divided by magnification, so we would do 0.

84 divided by 7,000, which gives us 0.

00012, and written a standard form, that's 1.

2 times 10 to the minus four.

Now what I would like you to do is convert your answer into micrometres.

Hopefully this is the easier bit.

We just need to times that answer by 1,000, which gives us 0.

12 micrometres.

Great job if you manage to get those right, well done.

We're ready now to move on to the final task of the lesson.

In each question you've been asked to calculate the magnification and you've been given a length of that organism and also an image size, so you need to make sure that the units are the same and then calculate the magnification.

Then in the second part of the task, you're going to complete the table, give your answers for the size of the images in standard form.

We need to use the equations that we've been using to calculate either the image size or the magnification, and we're going to give the image size in micrometres and millimetres in standard form.

And for the final part of task C, you've got three more calculations to have a go at.

I'm sure you're gonna do a great job.

Press pause and then play when you are ready for me to go through the answers.

Let's see how we did.

So for the first question, we have to do a conversion first.

So 14 times by 1,000 is equal to 14,000, that gets us into the correct units, and then we need to do 14,000 divided by 0.

7, which gives us a magnification of 20,000.

The second part, we have to do 17.

5 converted into millimetres, so we times it by 10, which gives us 175 millimetres, and then we do 175 divided by 1.

4, which gives us a magnification of 125.

And then for the question three, we have to do again a conversion from centimetres to millimetres.

So two times 10 gives 20 millimetres, then we divide that through by 0.

5 to give us a magnification of times 40.

Good job if you got those right.

Then for the table in part four, the size of the image in micrometres is 4.

25 times by 10 to the five, and then we will divide that by 1,000 to get millimetres, which is 4.

25 times 10 to the power of two.

For the second row, the size of the image of millimetres is gonna be five times by 10 to the zero.

We divide through by 1,000, and then the magnification is 25,000 For row three, the size of the image is 3.

75 times 10 to the power of four.

And then again we divide through by 1,000 to get 3.

75 times 10 to the power of one.

And then in the final row, the size of the image is one times by 10 to the one, and the magnification is times 20.

Really great job if you managed to get those right, well done.

And then moving on to question five, we should have 6.

75 times by 10 to the minus two, which is 0.

0675 metres, and then we do 0.

0675 divided by the magnification, which is 50 to give us 1.

35 times 10 to the minus three metres.

For number six, we do 250 times by 20 to give us 5,000 nanometers, and 5,000 nanometers written in standard form is five times by 10 to the power of three.

And then finally for number seven, 5,000 divided by one million gives us 0.

005 millimetres.

And then 0.

05 times by 15,000 is equal to 75 millimetres.

Some of those questions were really challenging, so you've done an absolutely brilliant job if you've managed to get them right.

If you need to pause the video to add any detail into your answers, please do.

If not, let's summarise everything we've learned this lesson.

So today we've been looking at the size and scale of cells, including standard form, and we said that most animals and plants are made up of millions or billions of cells.

Cells are too small to see with the unaided eye.

Therefore, we need a microscope.

We can compare the sizes of eukaryotic and prokaryotic cells and their subcellular structures using the same units, and we can calculate magnification using the real size and the image size of a magnified image using the following equation.

Magnification equals the size of the image divided by the size of the real object.

You've done a really great job this lesson.

Some of the things that we've been doing have been very complicated, so well done If you've got to the end and you've managed to get lots of the questions right.

I've really enjoyed today, I hope you have too and I look forward to seeing you next time.

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