Video Transcript
Place Value of Five-Digit
Numbers
In this video, we’re going to learn
how to represent five-digit numbers with place value tables and counters. We’re also going to learn how to
say what each digit in a five-digit number’s worth. Let’s start by modeling a
five-digit number.
In this example, it doesn’t really
matter what it is. So, let’s just choose five digits
to put in our place value grid. There we are. Now, hopefully, you already know
the value of four of our five digits. If we start by looking at the place
that has the least value, it’s of course the ones. And we could use five ones counters
to represent the five ones that we have here. Next comes the tens column, and we
have three of these. The digit two is in the hundreds
place. The next place along has a value of
thousands, so we need three 1,000 counters. And these are the columns that
we’ve learned before when looking at four-digit numbers, thousands, hundreds, tens,
and ones.
But now we have a new column to
think about. And as we know that each column has
a value that’s 10 times greater than the column on its right, we know that our new
column is going to have a value 10 times as great as 1,000. And this makes it easy to
remember. It has a value of 10 1,000s. In other words, if we made a tower
out of 10 1,000s blocks, this would be the same as one lot of 10,000, something like
this, which is huge. And it’s also the reason why we’re
using place value counters in this example and not blocks.
So, let’s show seven in the ten
thousands place by using seven counters with a value of 10,000 each. Now, as we’ve said already, a large
part of this video is just about understanding what the value of each digit in a
five-digit number is. And most of that is about building
on skills we already have because we should already know what the value of digits in
a four-digit number are. So, in a way, this is a little bit
of a revision lesson going over facts we already know but then being introduced to
one more column.
And let’s start with that column to
begin with. What’s the seven in this number
worth? Well, we could give two different
answers here. We could say that the place value
of the seven in this number is ten thousand. This seven is worth seven lots of
10,000. It’s in the ten thousands
place. But what is seven lots of 10,000
worth? What’s the value of this digit in
this position? We could skip count in ten
thousands seven times to find the answer. And although this might sound like
large jumps to make, if you can count in tens, you can count in ten thousands. Here we go. 10,000, 20,000, 30,000, 40,000,
50,000, 60,000, 70,000. The seven in the ten thousands
place has a value of 70,000.
In the next column, we can see the
digit three. But did you notice there’s another
three in our number too? These digits are exactly the
same. But because they’re in different
positions, they’re worth different amounts. Which is worth the most? As we’ve seen already, if we look
at the places in a number from right to left, the value of those places
increases. So even if we didn’t know that one
of our threes was in the thousands place and the other one was in the tens, we could
spot which one was worth the most because it’s the one further to the left. Three lots of 1,000 is 3,000, and
three 10s of course are worth 30.
Let’s complete the value of our
missing digits then. Two in the hundreds place has a
value of 200, and the digit in the ones place is worth five. So, we could read this number by
first looking at the ten thousands and the thousands digits and reading them
together as a number of thousands and then reading the last three digits as a
three-digit number. It’s the number 73,235.
Let’s have a look at one more
example.
What’s the largest digit in our
number? It’s nine, isn’t it? You can’t get a digit larger than
nine. But even though it’s the largest
digit, is it worth the most in this number? Well, we can see that it’s in the
ones place. So, this digit only has a value of
nine. But interestingly, in this number,
it doesn’t have the smallest value. Can you see why? This number contains a zero in
it. And a zero in the tens place or any
other position is worth zero. Our four digit is in the hundreds
place. This makes it worth 400. In the thousands place, we have a
seven. This has a value of 7,000.
But what about the digit one? It’s such a small digit. But where it is in this number
gives it the greatest value. It’s in the ten thousands place,
isn’t it? It has a value of 10,000. So, what’s our number? 17,409. And understanding the value of each
digit in this number helps us to say it in words, just like we’ve just done.
Let’s answer some questions now
where we have to put into practice everything that we knew already about thousands,
hundreds, tens, and ones, but also everything that we’ve learned about this fifth
place, the ten thousands column.
What is the place value of the
eight in 81,374?
This question gives us a five-digit
number made up, unsurprisingly, of five digits. And we’re asked what the place
value of one of them is, and that’s the digit eight. We know that place value is the
value given to different digits based on their position or place in a number. They may be worth ones or
hundreds. It all depends on their
position. And so this question is really
asking us, what’s the value of the place where the digit eight is sitting in this
number?
Probably the most useful thing we
could do to help us answer this question is to put this number into a place value
grid. And as we write each digit, we can
think about what they’re worth. We know that the value of each
place in a number is greater as we move from right to left. So if we look at where the eight is
in our number, perhaps the first thing we could say is that it’s in the place with
the greatest value in this five-digit number. But what is this place worth?
We know that the digit four is in
the place with the least value. It’s in the ones place. Then comes the tens, the hundreds,
the thousands, and the fifth column along to the left. Well, this column is going to
behave just the same as all the others. It’s going to be 10 times as great
as the last column. And because the last column is
thousands, we know the digit eight is in the ten thousands place. The place value of the eight in
81,374 is ten thousands.
Find the value of the digit two in
the number 27,940.
In this question, we’re given a
five-digit number. And we know that the position of
each one of these five digits really matters. It’s what gives them their
value. And we’re asked to find the value
of one of these digits. It’s the digit two. Can you see it right at the
beginning, on the left? To help us find out what this digit
two is worth, let’s model our number using place value counters.
The place with the lowest value is
all the way on the right here. It’s the ones place. And there are zero ones, so we
don’t need any counters. Next comes the tens place. The digit four is in the tens place
in this number. So, we could use four 10s
counters. And we know that four 10s are worth
40. The digit nine is in the next place
along. This is the hundreds place. And nine lots of 100 means this
digit has a value of 900. After the hundreds comes the
thousands place. The digit seven is in this
place. And seven lots of 1,000 is worth
7,000. So, we’ve slowly been building our
number up all the way to the digit that really matters. This is the digit we’re being asked
about.
Which place is the digit two
in? After the thousands comes the ten
thousands place. And because the digit two is in
this position, we’re going to need two counters, each worth 10,000. Now to find out what this digit is
worth altogether, we’re going to have to count in ten thousands twice, one for each
counter. And if we can count in tens, we can
count in ten thousands. It’s just as easy, 10,000,
20,000.
We’ve used our knowledge of place
value to understand that the digit two is in the ten thousands place in this
number. And that’s how we know the digit
two isn’t worth two or 20 or 200. The value of the digit two in the
number 27,940 is 20,000.
Chloe makes a five-digit number out
of the digits nine, eight, six, four, and one. She says, “Out of my five digits,
nine is the greatest. So I know it has the greatest value
in my number.” Is Chloe correct?
The answer to this question is
either going to be yes or no. But for us to know which one of
these is correct, we’re going to need to understand something about place value. Firstly, let’s look at the
five-digit number that Chloe’s made. The picture shows us the way that
she’s arranged her digit cards. Now, where’s that number nine? If we’re reading from left to
right, we could say that Chloe’s put it in the last position, the place furthest to
the right. At the moment, this has a value of
nine. The number that she’s made is
18,649. But is it still worth nine if she
swaps it with the six? Or if she moves it to where the one
is?
We know that the position of a
digit in a number really affects how much it’s worth. So, if she did move the number nine
in all these different positions, it’s going to be worth different amounts. Where it is at the moment is in the
ten thousands place; it’s worth 90,000. Let’s put our number back to how it
was. Now, what we’ve just talked about
is really important. The value of each digit in a number
doesn’t just depend on what that digit is, but also where it appears in the number,
whether it’s in the ones place, the tens, the hundreds, thousands, or the ten
thousands place.
Now, let’s remember this as we read
what Chloe has to say about this number. Now, she says two sentences. Firstly, “Out of my five digits,
nine is the greatest.” Now, we can’t really argue with
that, can we? The digits were listed right at the
start of the question: nine, eight, six, four, and one. And what she said is true. Out of those five digits, nine is
the greatest. But she then goes on to say
something based on this. And that little word “So” at the
start of the sentence is important. She’s saying because nine is the
greatest of my five digits, I know that it has the greatest value in my number. In other words, I think the value
of a digit is just based on what that digit is, nothing else.
Well, we know this isn’t true at
all, is it? The place that a digit appears in a
number also affects its value. We know that in a five-digit
number, the place with the greatest value is the ten thousands place on the left
here. And so, interestingly, even though
it’s the smallest digit, the digit with the greatest value in Chloe’s number is the
digit one. It’s in the ten thousands
place. And so even though we know Chloe is
right when she says, out of her five digits, nine is the greatest, we also know that
for it to have the greatest value in Chloe’s number, it would need to be in the
place with the greatest value, and it’s not. And that’s why we can answer, no,
Chloe is not correct.
So, what have we learned in this
video? We’ve learned how to represent
five-digit numbers using place value tables and counters. We’ve also learned to state the
value of each of the five digits.
