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Hello, and welcome to this lesson.

My name is Mr Maseko.

In this lesson, we're looking at number systems. We're going to be looking at writing based ten numbers and different basis.

Now we'll find out what all that means during the course of the lesson.

Before you start the lesson, make sure you have a pen or a pencil and something to write on.

Okay? Now that you have all those things, let's get on with today's lesson.

First try this activity, there's two students wrote these two sentences.

Antony says I can see that one ten is ten times greater than one one.

And the second student says I can see that 1000 is 100 times greater than one ten.

Now how many sentences can you write using that diagram? Pause the video here and give that a go.

Okay.

Now that you've tried this, now that you've tried this let's see what you have come up with.

Well, what could we have said? Well, let's look at the relationship between one ten and 100.

Well, 100 is ten times greater than one ten.

Well, what else could you have said? Well, if we look at the relationship between a thousand and a one, well, 1000 is 1000 times greater than one one.

Now what we're looking at today is what we call base ten.

And other base systems for our number systems. Now what is base ten? It's all about place value in base ten, each place value is a power of ten.

Cause if you look, we always start with our wants column so every number system has a ones column, cause we need to be able to count in singles.

But the next place value up, depends on what base you're in.

In base ten, we go from the ones to the tens and then from the tens to the hundreds and then from the hundreds to the thousands.

So, to go from place to place on your place value chart, you always multiply by ten.

And that's why this is called base ten.

So if you look at a typical number like this, which is 2349, or what can you see? Well, in this, what we have is we have two thousands, three hundreds, four tens, and nine ones.

Now Here we have 24 written in base ten.

Now this stop scripts don't have, this is to show what base we are in.

So if you look that just tells us when base ten, usually we don't have to write it, but because we're dealing with numbers written in different bases, we have to specify what base we had written our number in.

And then if we look at this, this says this is 24 written in base five.

Now what could that mean? We know about this means this number has two tens.

This number has two tens because the two is in the tens column in base tens and four ones.

Cause the four is in the ones column in base ten.

But here we have four, four.

Notice how I didn't say 44.

We have four, four and base five, which also means 24.

Well, let's look at a place value chart for base five what would we have? we'll have our ones column and then what will come after, what we multiply by it? Because the next place value, we have the ones it's base five so we multiply by? Good! So we multiply by five.

So, this becomes a five column.

So the next one will be our 25 column.

And then the next one will be our 125 column, to go from place to place on your place value chart in base five, you multiply by a five.

In base ten, you multiply by ten.

Although in intuitive, so what does this mean? What does four four mean? Well, this means we have, well, that four is in the fives column.

So we have four fives.

And what else? And we have four ones.

Well four fives, well four multiplied by five, what does that give you? That gives you 20 and four multiplied by one, that gives you four, 20 add four that gives you 24.

So we've represented 24, which in base ten, we've represented it in base five cause this is four fives and four ones.

Can you do the same thing for 28? Right back in base five.

Pause the video here and give that a go.

Okay.

Now that you've tried this, let's see what you come up with.

If you think of 28 how many fives do we have in 28? How many fives? well have five fives or five fives is what? five fives is 25.

So we can see that in our place value chart, we have at 25 column for best five.

So we know that we have at 25 and it was left over well, or we're left with three.

So we have a 25 and three ones.

So.

Would I write it like this? No, I would invite this because just the same way as in base ten, if we are, if we have a place value that has no value in our number.

We have to use our placeholder, which is a zero.

So this is an edge we would write, we have three ones, we have zero fives and we have one 25.

So if you look at this, that could be 28 written in base five.

So let me write out, I'm going to to write a subscript five to show that that's us written in base five.

How do we know? this has one 25, one times 25 is 25 and three ones, three times one is three, 25 and three gives you 28.

Well, let's try this again.

This time we are in a different base.

So we have 24, which in base ten we've seen already.

And what is written at base seven is written as three three.

One of the plays values for base seven.

Well, we have the ones column, the sevens column, the 49 column, and then the 243 column.

So ones, sevens, 49s and then 243 column and then they'll still just keep going.

So remember to go from place to place and base seven would multiply by Good.

Seven.

So what does three three mean in base seven? Well, three three in base seven.

That means that we have three sevens.

and we have three ones three sevens and three ones.

What's three sevens? three sevens is 21, three ones is three, 21 add three gives you 24.

And that's how you lost 24 and base 10.

We'll come to why we can, why we would want to write different numbers in different basis in a later lesson in the series.

But at this point, it's really interesting how we can identify what base we're in, based on the place value in our charts.

Now, how would you write 28 in base seven? So if you think about it, how many sevens do we have in here? We have four sevens, exactly four sevens.

So this has, would have zero ones and four sevens.

So this would be 28, which in base seven is four zero cause four sevens.

Now notice how don't say it's 40 because you have to be careful how you're staying your number when you are in a different base.

The way we say our numbers is, is based on what based ten.

Cause that's the one we use and why do we use base 10? Well, some people say it's because we have ten fingers.

In other cultures, they use different bases like in the Mayan number system they would use, they use base 20.

why do you think they use base 20? Well, they were just better with their toes than we are.

Ten fingers, ten toes.

I'm not going to show you my toes though.

But let's move on with this lesson.

So here's an independent task for you to try.

So here's some numbers, which in different bases.

Write them in base ten.

Pause the video here and give that a go.

Okay.

Now that you've tried this let's see what you've come up with.

Well, what do we have? We have two threes in base five so what does that mean? Or we've got two places, so I'm just going to use two place values of our base five.

So we've got our ones and our fives.

That's in base five.

So we have three ones and two fives.

What two times five, that is ten add three.

So two three in base five is 13 in base ten.

So this is the same as 13 in base ten or two one in base seven.

Well, again, we have two place values so that is, the ones and the sevens and we have one one and two sevens.

Two lots of seven is 14 add one this is 15 in base ten.

Three five in base eight.

Well, that is five ones and three eight, three eight gives you 24, five ones gives you five, So this would be 29 in base ten.

Four Zero in base five, well we know of four fives, So this would be 20 in base ten.

123 in base four.

Well base four, we haven't seen yet with their place values or base four with the ones, the fours and the 16s.

So what do we have? We have one 16th, one 16.

We have two fours and we have one one.

One 16 and 16, add two fours, that is eight, add one so this is 25 in base ten.

And then one zero, one zero in base tune well base tune is one two, four places.

It's the ones, the twos, the fours and the eights.

We have one eight, zero fours, one two and zero ones.

So that is, would be equal to ten in base 10.

Now looking at base two specifically, phase two is code binary.

And these, the place values for base two.

So you the ones, the twos, the fours, the eight, the sixteens of five to 60 fours.

And it keeps going.

So write each of the following numbers, these are all base ten numbers.

Write them all in base two.

And then you got to answer this question to write this number in base 10.

Pause the video here and give that a go.

Okay.

Now that you've tried this, let's see what you come up with.

Well, 24, what about the A written in base two? Well, if you think, how many twos do you have in 24? while you have.

What? 12 twos, but we can't buy 12 twos.

We know that in 24 we have one 16.

So we know that we have one 16.

16, so we're left with eight and we have one eight and then we have a zero fours, zero twos and zero ones.

So there should be 24 in base two over 32.

But in 32 we have one 32 and then zero sixteens, zero eight, zero fours, zero twos and zero ones.

See how base two takes really two digit numbers and they end up being what? Multiple digit numbers, much greater than two.

Now 35 or 35 is one 32 zero sixteens, zero eight, zero fours, zero twos.

and then Nope, not zero twos.

One two and one one.

Cause we can't have three ones, Cause three ones contains one two.

So we have one two and one one.

What about four? Well, four is one four and zero twos and zero ones.

And then 64 or 64 is one 64, zero 32 zero 16, zero eight zero four zero twos and zero ones.

And then 128.

Well, if you increase, go up one more step.

We have a 128 column.

So you have 128, zero 64s, zero 32s, zero 16, zero eight, zero fours, zero twos, zero ones.

Now why would anyone want to ride numbers like this? We will talk more about binary coding, it's uses in lesson four of this series.

But why do you think base two is called the binary system? Like bicycle it's like bicycle has two wheels.

Binary is because it only has two they're just like up here.

It's all either zeroes and ones.

And that's really important the fact that it's only zeros and ones is really important, as some really quick applications in the real world.

Now, this number we're going to ride this in base ten.

So let's look at our place volume this is all ones we got one one, zero twos and one four, so one, one, one four makes five and then zero eights, zero sixteens, zero 32s.

So we got 64 add five, so this number is 69.

Now really well done for getting through this lesson.

And I hope you've learned something really interesting or writing numbers in different basis.

If you want to share some numbers that you written down in different basis, ask your parent or carer to share your work on Twitter, tagging at Oak National and hashtag LearnwithOak.

Bye for now.