Video Transcript
Writing Five-Digit Numbers in
Various Forms
In this video, we’re going to learn
how to write five-digit numbers using digits, words, as well as in unit and expanded
form. If we’re going to write five-digit
numbers in different ways, we’re going to need to understand what each of those
digits is worth. So let’s quickly go over our
knowledge of place value.
The digit with the smallest value
in a five-digit number is the ones digit, over here on the right. Now, in this column, we can show
anywhere between zero ones up to nine ones. But this column only holds one
digit. So as soon as we get to 10 ones, we
need to regroup them because 10 ones are exactly the same as one 10. Again, our tens column can fit
anywhere between zero and nine 10s. But as soon as we get to 10 10s, we
move along to the next column again and regroup because 10 10s are the same as one
100. And we can use this idea of each
new place to the left being worth 10 times as much as the last one as we move along
through the columns. We know that 10 100s are the same
as one 1,000. These are the place value columns
in a four-digit number.
But what do you think the value of
our fifth place is going to be? Because we know how place value
works, we know that it’s going to have a value of 10 1,000s. And 10 1,000s have the same value
as one lot of 10,000. This is the new column that we’re
gonna be thinking about in this video. Five-digit numbers contain a number
of ten thousands, thousands, hundreds, tens, and ones.
Now, if you remember what you’ve
learned about your work with four-digit numbers, you’ll remember that when we write
larger and larger numbers, we don’t just write long strings of digits. We often group them in threes to
make them easier to read. The hundreds, tens, and ones digits
are in a group of three. We call this the ones group. And we did say the thousands digit
is in a group of its own, but now we’ve got a new digit to add to this. Both the ten thousands and
thousands digits are in the next group along.
And while sometimes you might see a
little gap between the thousands and the hundreds digits to show these groups, in
this video, we’re going to be using commas. It really helps us to say
five-digit numbers aloud because as soon as we see that comma, we can say
thousand. So this number here, for example,
is 10,360.
Now, before we move on, you may be
wondering why we’ve just used place value counters and not place value blocks when
we’ve done so much work with them till now. Well, it’s because as we work with
larger and larger place values, we need larger and larger blocks. We’d need 10 of these 1,000s cubes
to make some sort of a rod. This is what a 10,000s rod might
look like. It’s really too big to use. And we’ve learned enough about
place value so far to understand what ten thousands are. We don’t need to visualize them
like this. And so, in this video, we’ll just
be using place value counters if we have to.
To understand all the different
ways we can write five-digit numbers, we’re going to need a five-digit number. So let’s model one out of
counters. Let’s have five 10,000s, two
1,000s, seven 100s, four 10s, and nine ones. The first way that we could write
our five-digit number is by recording all these place value units that we can
see. As we’ve just said, we’ve got five
10,000s, two 1,000s, seven 100s, four 10s, and nine ones. By recording the number of ten
thousands, thousands, hundreds, tens, and ones that we have, we’ve written our
number in what we call unit form. It’s a way of showing all the
different place value units that make up our number.
How else could we represent this
five-digit number? If we’re looking for the quickest
way to show a five-digit number, we don’t want to be modeling it with lots of
different place value counters or even writing it in unit form. The quickest thing we can do is
simply to write four digits. There are five 10,000s, so we need
to write the digit five in the ten thousands place, two 1,000s. Now we’re about to move on to our
hundreds. Remember what we said about
separating our thousands and hundreds digits? That’s right, a comma.
We have seven 100s, so the digit
seven goes in the hundreds place, then four 10s and nine ones. To write our number using digits,
we just need to write five-two-seven-four-nine. But that’s not how we’d say this
number if we saw it. How would we say or write this
number in words?
Well, this is where that comma
comes in useful. Because we did say that our ten
thousands and thousands digits are read as a number of thousands. When we get to the comma, we say
thousands. To the left of the comma then, we
have the digits five and two, five 10,000s and two 1,000s. Put them together and we’ve got
52,000. Then we just read the hundreds,
tens, and ones as if we were reading a three-digit number. Our number in words is fifty-two
thousand seven hundred forty-nine.
Now, in this video, there’s one
more way of representing five-digit numbers that we’re going to look at. And this is expanded form. When something expands, it grows;
it gets bigger. And when we write a number in
expanded form, we separate it out into each of its parts. Instead of writing it using five
digits, we expand it out and write down what each of those digits is worth. And we write the number as an
addition.
A good way to show this is using
arrow cards. Here’s our number modeled out of
arrow cards all put together. But then we can expand this out and
pull out each individual arrow card and see what they’re worth. As we’ve said already, the five
digit is in the ten thousands place. This is the same as five lots of
10,000. 10,000, 20,000, 30,000, 40,000,
50,000. The digit two is in the thousands
place. This has a value of 2,000. The seven digit has a value of
700. Four in the tens place is worth
40. And of course nine ones are simply
worth nine.
So using expanded form, we’d say
our number as an addition, adding all these parts together. It’s worth 50,000 plus 2,000 plus
700 plus 40 plus nine. So if we include our place value
model that we started with, we’ve written a five-digit number in five different
ways. And we don’t even have to stop
there. We could even use something like an
abacus to show our number.
Let’s have a go at answering some
questions now where we have to read and write five-digit numbers in different
ways.
Write eighty thousand nine hundred
twenty-seven in digits.
There are lots of ways to represent
numbers. And in this question, we’re given a
number that’s been written in words: eighty thousand nine hundred twenty-seven. And we’re asked to write this
number a different way, in digits. How many digits do you think we’ll
need? Or perhaps a better question is,
which part of our number should we look at to work out how many digits we’ll
need?
Just like any number, as we read it
in words, we can see that the place value units get less and less. So, for example, the last number we
say, which is the seven in 27, this actually has the smallest place value. This isn’t really a lot of help to
us to work out how many digits we’re going to need. But if we look at the other end of
our number, that’s the first part that we say, we can see a different story,
80,000. This is the part of the number with
the largest place value.
Now, because we can see the word
thousand, it might look like we’re talking about the thousands column here. Is this a four-digit number? Well, when we look how many
thousands we need, it’s 80,000. We’re going to need five digits to
show our number. Let’s draw a place value grid to
show this.
If our number was 8,927, then we’d
need to write the digit eight in the thousands place. Then it would be a four-digit
number we’d be talking about. But we need to show 80,000. And so the digit eight needs to go
in the ten thousands place. Eight lots of 10,000 are the same
as 80,000. And notice that our number doesn’t
say 81,000 or 85,000. It just says 80,000. So we need to put a zero in the
thousands place.
Now we’re just left with the
hundreds, tens, and ones, and we need to show 927. Well, we know how to do this, don’t
we? That’s a nine in the hundreds
place, a two in the tens place that represents 20, and a seven in the ones
place. And the only other thing that’s
useful to remember as we write our five-digit number is that it’s helpful to put a
comma after the thousands digit and before the hundreds digit. It’s just a way of separating out
the thousands, and it helps us to read the number quickly, 80,927.
We used a place value grid to show
that this number contains eight 10,000s, zero 1,000s, nine 100s, two 10s, and seven
ones. We can write the number using the
digits eight-zero-nine-two-seven.
Write this number in words.
In this question, we’re given a
five-digit number. And it’s a good job it wasn’t read
to you as we read the question. Then you’d know how to write this
number in words straight away. But so far, all we’ve got is this
number written in digits.
To work out how to write it in
words, we’re going to need to think about the place value of each of these
digits. What are they worth? Let’s try modeling our number using
place value counters. Let’s start with the lowest-value
digit first. So we’re going to need one one, six
10s, six 100s, eight 1,000s, and our largest-value digit, six lots of 10,000. So how would we read this
number?
To begin with, what are six lots of
10,000 worth? 10,000, 20,000, 30,000, 40,000,
50,000, 60,000. Let’s make a note of this,
60,000. But wait a moment! We’ve got some more thousands. There’s an eight in the thousands
place. Our number isn’t just 60,000; it’s
68,000. Perhaps you noticed a little comma
in the number in the question. This comma appears between the
thousands and the hundreds digits, and it’s a way of separating out the
thousands. So when we see this comma, we can
look at it and say thousand, sixty-eight thousand.
Now we just need to say the last
three digits. We’ve got a six in the hundreds
place, so that’s six hundred, six 10s, which are worth 60, and then our one one. Because we read our last two digits
as a two-digit number, we say sixty-one. Perhaps you knew how to write this
number without even using the place value counters to help. A five-digit number that’s written
68,661 is written in words sixty-eight thousand six hundred sixty-one.
What is 10,000 plus 2,000 plus 50
plus five in standard form?
In this question, we’re given what
looks like an addition, but this is more than an addition. This is a number that’s been
written for us in what we call expanded form. Expanded form is a way of writing a
number as an addition by showing the value of each of its digits. So we can see with the number
that’s being talked about here we’ve got a digit that’s worth 10,000. There’s going to be another digit
that’s worth 2,000, one that’s worth 50, and then a digit that’s worth five.
Now, we’re asked to write this
number in standard form, in other words, the way that we usually write a number
using digits. Because there are four parts to our
addition, do you think it’s gonna be a four-digit number? Well, if we look closely, we can
see that there’s one type of digit missing. Did you spot it?
Let’s use a place value grid to
help us see which one. The first number in this addition
is 10,000. So we need to use a digit that
represents this value. To show 10,000, we need to write
the digit one in the ten thousands place. One lot of 10,000 is 10,000. The next number in our addition is
2,000. So which digit do you think our
number has in it and where should we write it?
Well, for a digit to be worth
2,000, it needs to be the digit two and it needs to appear in the thousands
place. Our next number is 50. How would we represent 50 in our
place value grid? 50 is the same as five 10s. So we need to write the digit five
in the tens place. Can you see what’s happened
here? We haven’t been given a number of
hundreds. We still need to show that there’s
an empty hundreds place though, and so we can use zero as a placeholder. And that’s why even though we’ve
been given four parts to our addition, it’s actually a five-digit number. We just don’t have any
hundreds. Finally then, we need to add
five. And to show five in our number, we
just write five in the ones place.
We recognized that the addition in
the question was a number written in expanded form. To write this number in standard
form, we thought carefully about how to create these values by writing digits in the
right places. The number is 12,055. And we write this in standard form
by writing the digits one-two-a comma-zero-five-five.
What have we learned in this
video? We’ve learned how to write
five-digit numbers using digits, words, and in unit and expanded forms.
