Video Transcript
Comparing Five-Digit Numbers
In this video, we’re going to learn
how to compare whole numbers with up to five digits. And we’re going to do this by
thinking carefully about the place value of each digit.
The Penguins are a world famous
rock band, and they’ve recently put out two new records. There’s what they like to call the
Blue Album. And it might seem like a funny name
for a record, but this one’s called the White Album. Now both of these records are quite
popular. We can tell this because underneath
the picture of each record, we can see that total sales. And each of these is a five-digit
number. The Penguins must have a lot of
fans. Let’s read each number. The Blue Album has sold 63,152
copies, and the White Album has sold 63,125 copies. But which record is most popular;
which has sold more?
To find the answer, we need to
compare these two five-digit numbers and find out which is larger. Now, we know that when we compare
two numbers, we need to look at the digits that make them up, and we need to look
from one number to the other. At the moment, our two numbers are
side by side. Now, we could compare them by
looking across from one to the other. But there’s a much better way. By writing each of our numbers in a
place value grid, we’ll be able to compare the value of each digit from ten
thousands to thousands, hundreds, tens, and then ones. If we want to compare the place
value of digits, looking up and down is much easier than looking across.
To begin with then, let’s complete
the total sales for the Blue Album, and we said that this’s sold 63,152, and the
total sales for the White Album, 63,125. Lots are similar digits there,
aren’t there? Now, if we’re going to compare
these two numbers together, which digit are we going to start with? Shall we start by comparing the
ones digit and then work our way from right to left? Or shall we begin with the ten
thousands digits and work from left to right? Well, we know from our experience
comparing smaller numbers that we always begin with the digits that are worth the
most. And the digits that have the
largest place value in these two numbers are the ten thousands digits.
So, we’re going to start with this
column and work our way from left to right by looking at our numbers place by place
or column by column, it’s almost like we don’t need to worry about the rest of the
number. We just need to focus on the one
column we’re looking at. So, let’s cover up all the other
digits and just focus on the ten thousands digits.
Now, we can see straightaway that
both numbers contain a six in the ten thousands place. We can’t separate out one number as
being larger than the other, can we? They’re both clearly sixty
something thousand and something. So, what do we do? We move on to the next column
along. The number 63,152 has a three in
the thousands place. Oh, but so does the number
63,125. Both our numbers are sixty-three
thousand and something. We still can’t separate them out
and see which is larger.
On to the hundreds digits. Both numbers have a one in the
hundreds place. So far, they’re exactly the
same. But thankfully, as soon as we get
to the tens digit, we can see a difference. The Blue Album has sold 63,152. So, in the tens place, there is a
digit five. And the White Album has sold
63,125. So, this has the digit two in the
tens place.
We’ve worked our way along the
number, comparing the place value of each digit from those that are worth the most
to those that are worth the least. And now that we’ve found two digits
that are different, we can compare the numbers. It really doesn’t matter what the
ones digits are. Because the first number has five
tens and the second number has two tens, we can tell the first number is larger. 63,152 is greater than 63,125. And that’s how we know out of these
two records, the Blue Album has sold more.
Let’s have a go now at answering
some questions where we have to compare numbers together and we’ll use a place value
grid each time to help us.
Use the symbol for is less than, is
equal to, or is greater than to compare the numbers on each pair of cards. 23,099, what, 23,851; 11,273, what,
9,768; and then finally 25,938 plus 1,000, what, 26,819 plus 100.
In this question, we’re given three
pairs of cards, and we’re told that we need to compare the numbers on each pair. Let’s start with the first two
numbers. How are we going to compare
these? Well, we know that to compare two
numbers means to look at the digits in those numbers and their place value. And a good way of doing this is
using a place value grid. Let’s sketch one for these numbers
by writing both numbers in the grid on top of each other. We can compare them digit by
digit.
So, our first number has a digit
two in the ten thousands place, three in the thousands place. It has zero hundreds, nine tens,
and nine ones. It’s 23,099. The number on the second card also
has five digits, and some of these digits are very similar. There’s a two in the ten thousands
place, a three in the thousands place. This particular number has an eight
in the hundreds place, a five in the tens place, and a one in the ones place.
Now that we’ve recorded both of our
numbers in a place value grid, it is going to be a lot easier to compare them digit
by digit and. To do this, we need to begin with
the digits that have the largest value. These are the digits that have the
most effect on the number. In other words, we need to start by
looking at the ten thousands place. Both our numbers have the digit two
in this place, so we can’t separate one number as being larger than the other just
by looking at this digit. We’re going to need to carry on and
look at the next digit alone. If we compare the two digits in the
thousands place, we can see that these are the same too. We still can’t separate out our
numbers.
We’re going to have to compare the
hundreds digits. Thankfully, we can see that these
are different. And so, we now can tell which of
our numbers is larger. The number on the first card has a
zero in the hundreds place, and the number on the second card has an eight in the
hundreds place. And it doesn’t matter about the
tens and ones. We know which of our numbers is
larger just by looking at the hundreds digit. Our second number is greater than
the first. But of course, when we compare two
numbers, we read them across from left to right. So, we need to use the less than
symbol. 23,099 is less than 23,851.
Now, let’s compare our second pair
of cards. Now, we could use a place value
grid again to compare these numbers, but can you see something interesting about
them? They both have a different number
of digits. This is going to make them really
quick to compare. In fact, we don’t really need to
use the place value grid. Our first number has five digits,
so the highest value digit is a ten thousands digit. But our second number only has four
digits. So, the highest value digit is only
worth thousands.
A whole number with five digits is
always going to be larger than a whole number with four digits. So, as we read our numbers from
left to right, we’re going to need to use the symbol is greater than. 11,273 is greater than 9,768. And if we complete our place value
grid, we can see that the first number has a one in the ten thousands place. But our second number doesn’t have
anything.
Now, let’s compare our final pair
of cards. These are interesting because each
one has an addition written on it. For us to compare these values,
we’re going to need to find the total on each card. On our first card, we have 25,938
plus 1,000. Now, what happens if we add 1,000
to a number? Well, there’s a change to the
thousands digit. The number 25,938 has a five in the
thousands place. But if we add one more 1,000, that
five is going to become a six. So, the value of our first card is
26,938.
The addition on our second card is
26,819 plus 100. And we know when we add 100 to a
number, it’s the hundreds digit that changes. 26,819 has the digit eight in the
hundreds place. But if we add one more 100, our
number will contain nine hundreds. So, the value of this particular
card is 26,919. This time, both of our values have
the same number of digits. So, we’re going to need that place
value grid again.
Starting with the place that has
the largest value, we can see that both numbers have a two in the ten thousands
place, so we can’t separate them out yet. If we compare the thousands digit,
these are the same, so will a hundreds digit. But we can see that that the tens
digit are different. And this helps us now to compare
the two numbers. 26,938 has a three in the tens
place, and 26,919 only has a one in the tens place. That’s how we know the value on the
first card is greater than the value on the second.
We’ve used place value grids and
also in the second example our knowledge of the number of digits to help us compare
the numbers on these pairs of cards. 23,099 is less than 23,851. 11,273 is greater than 9,768. And the value of 25,938 plus 1,000
is greater than the value of 26,819 plus 100.
Fill in the blank using the symbol
for greater than, less than, or equal to. Forty-five thousand six hundred
fifty-eight what forty-five thousand two hundred fifty-eight.
In this question, we’re given two
numbers to compare. Now, usually, when we compare
numbers, we might look at each digit one by one, see what they’re worth. But in this particular question,
our numbers have been written in words. How are we going to compare
them? Well, one way to find the answer
might be to draw a place value grid and to actually write each number in digits. Our first number is 45,658, and our
second number is quite similar, 45,258. Because our numbers are so similar,
as well as comparing them using the place value grid, we could actually compare the
words together. Let’s do both at the same time.
When we compare two numbers
together, we know that we always start by comparing the digit with the greatest
value. And as these are two five-digit
numbers, that digit is in the ten thousands place. Both numbers have a four in the ten
thousands place. So, we need to go on and look at
the thousands place. But they have the same digit here,
too. And if we compare our numbers
written in words, we can see this. Both numbers begin with forty-five
thousand.
We’re going to need to compare the
next digit along. That’s the hundreds digit. Our first number has a six in the
hundreds place, but our second number has a two. And we can see this difference if
we compare the numbers in words. Our first number is forty-five six
hundred and something, but our second number is forty-five two hundred and
something. It doesn’t matter about the rest of
the number. We can compare these two numbers
together, just using the hundreds digits. Six is greater than two. So, we know 45,658 is greater than
45,258. The correct symbol to use in
between these two numbers to compare them is greater than.
Now, so far, we’ve had a go at
comparing five-digit numbers using place value grids. But we can also compare a pair of
numbers using a number line. We can estimate where each one
belongs. Let’s have a go at comparing two
numbers where we use this method.
Is 21,442 less than, equal to, or
greater than 21,942?
In this question, we’ve got two
five-digit numbers to compare. But did you notice something about
these numbers as we read them? They both begin with the same
number of thousand, 21,000. It’s only the last part of each
number that’s different. This means the numbers must be
quite close together. We could use a number line to help
compare them.
If both numbers are twenty-one
thousand and something, they must come somewhere between 21,000 and 22,000 on a
number line. When we’re using a number line like
this is always helpful to mark the midway point. And that’s 21,500. So, where does our first number
belong on this number line? Where would you put 21,442? Well, twenty-one thousand four
hundred and something is just less than 21,500, our midway point. We could estimate that this number
is about here.
Now, where does our second number
belong? Again, the digit we need to be
looking at is the hundreds digit. We know that the ten thousands and
the thousands digits are the same. This number is twenty-one thousand
nine hundred and something. This is very close to 22,000, isn’t
it? And now, we can use our number line
to answer the question. We can see that 21,442 is less than
21,942. The correct answer to this question
is to use the symbol that represents less than.
What have we learned in this
video? We’ve learned how to compare
numbers with up to five digits by thinking about the place value of each digit.
