Video Transcript
Rounding Numbers up to One Hundred
Thousand
In this video, we’re going to learn
how to round whole numbers within one hundred thousand to any place value. We’re going to do this using number
lines and also by thinking carefully about the value of each digit.
Let’s start by imagining a farm
that’s a lot larger than your average farm. The number of sheep on this farm is
a massive 14,796. Now, every month the farmers get
together and have a chat about the size of each flock. And when this particular farmer
describes how many sheep he has, he doesn’t give the exact figure. No one really wants to know the
exact figure. Instead, he rounds it.
As I’m sure you know, rounding a
number is a way to say it more simply. We say it to the nearest ten or
hundred or thousand and so on. Because this is a five-digit
number, there are four possible ways we could round it. We can’t round it to the nearest
one; that doesn’t make sense. But we could round it to the
nearest ten, hundred, thousand, or even to the nearest ten thousand.
Let’s start by thinking about what
this number would be if we rounded it to the nearest ten. Now, there are going to be two
digits that are important to us here. One is the tens digit. This is going to give us an idea of
where the number belongs. But then also the digit to the
right of this is important. This is going to tell us whether to
round the number up or down.
The tens digit of 1,796 is a
nine. This digit shows us that our
five-digit number comes somewhere between 14,790 and the next multiple of ten after
this, which is 14,800. But which of these two multiples of
ten is our number nearest to? Should we round it up or down?
We’re using a number line to help
us here. And one of the important things
that we can do when using a number line is to mark the midway point. Then it can help us place our
number. And halfway between 14,790 and
14,800 is 14,795. Now that we’ve marked this halfway
point, we can see which side of it our number belongs. And what’s going to help us here is
the digit to the right of the tens place. Our number 14,796 is greater than
14,795. If we were to estimate its position
on this number line, perhaps it would be about here. And because it’s greater than the
midway point, we can round it up. The number of sheep on our farm,
rounded to the nearest ten, is 14,800.
Hopefully, you can see that if our
farmer was talking to his friends, it’s much simpler to be able to say, “Oh, I’ve
got about 14,800 sheep.” It’s a much simpler number. And I’m sure you’ve practiced
rounding two-, three-, and four-digit numbers before. But now that we’re rounding
five-digit numbers, we’ve got a new column to think about.
What if our farmer wants to
describe the number of sheep even more simply? What if he rounds it to the nearest
ten thousand? This is our new column with
five-digit numbers. But it’s just as straightforward to
round to the nearest ten thousand as it is to round to the nearest ten. Again, we really just need to think
about two columns. The ten thousands digit is going to
give us an idea of where our number belongs. And then the digit to the right of
this, which is the thousands digit, is going to tell us whether to round it up or
down.
So to begin with, the ten thousands
digit is a one. This tells us that the two
multiples of ten thousand that our number’s between are 10,000 and 20,000. And once again, if we mark the
halfway point, it’s going to help us. Halfway between 10,000 and 20,000
is of course 15,000. But where does our number
belong?
It’s time to look at the digit to
the right. Our number is 14,796. And so the thousands digit is a
four. 14,000 is less than 15,000. So perhaps we’d put it about here
on the number line. And because it’s less than 15,000,
we’re going to need to round it down. The number of sheep rounded to the
nearest ten thousand is actually 10,000. Depending on whether our farmer
rounds his sheep to the nearest ten, hundred, thousand, or ten thousand, he’s gonna
get a different answer. Just look at the difference between
these two numbers. If he rounds his total to the
nearest ten thousand, it’s gonna sound a lot less than if he rounds it to the
nearest ten. Doesn’t always work like this. But in this particular number, the
digits meant that we had to round down. It’s made a big difference.
Let’s try answering a couple of
questions now where we can use number lines to help us round some five-digit
numbers.
Look at the given number line. If we round 14,189 to the nearest
ten thousand, what do we get? If we round 14,189 to the nearest
thousand, what do we get? And if we round 14,189 to the
nearest hundred, what do we get?
Let’s start by doing what the first
sentence tells us to do, having a good look at the number line we’re given. We can see that on either end of
this number line, there’s a multiple of 10,000. We’ve got 10,000 at one end and
20,000 at the other. And there are 10 jumps or intervals
just like this one in between. So each interval must be worth
another 1,000. After 10,000, we have 11,000,
12,000, 13,000, and so on, all the way up to 20,000. The last thing to notice about our
number line is this speech bubble here. Inside it, we’ve got a five-digit
number. And it’s this five-digit number
that our three questions are based on.
Firstly, we’re asked, if we round
14,189, which is the number in the speech bubble, to the nearest ten thousand, what
do we get? Well, this number line is perfect
for answering this question. The nearest ten thousand is either
going to be 10,000 or 20,000. As well as thinking about the two
numbers at either end, it’s also important when using a number line to think about
the halfway point. And halfway between 10,000 and
20,000 is 15,000. And because 14,189 is about here on
our number line, we can see that it’s less than 15,000. The nearest multiple of 10,000 is
10,000 itself. We’re going to need to round this
number down. 14,189 rounded to the nearest ten
thousand is 10,000.
Next, we’re asked to round the same
number, but this time to the nearest thousand. Now, do you remember we said that
each interval on our number line was worth 1,000 more? So to find the answer to this
second question, we really just need to zoom in and think about part of our number
line, this part here. Let’s sketch a new number line to
show what we mean.
Now, we know from looking at our
first number line that the two multiples of a thousand that our number’s in between
are 14,000 and 15,000. And one of these is going to be our
answer. But before we start to think about
whether to round our number up or down, let’s mark that halfway point again. Halfway between 14,000 and 15,000
is 14,500. If we look at the hundreds digit in
our number, it’s a one. So where would we estimate it
belongs on our number line? Maybe somewhere like here? We know that fourteen thousand one
hundred and something is less than 14,500. So once again, we’re going to have
to round our number down. 14,189 rounded to the nearest
thousand is 14,000.
Finally then, we need to round our
number one more time, this time to the nearest hundred. If we split our previous number
line into 10 intervals just like before, each one would be worth 100. And the part of this number line
that we need to use to find the answer to this last question is this part here. Let’s zoom in to it. As we’ve said already, the hundreds
digit in 14,189 is a one. This tells us that the two
multiples of a hundred that our number’s in between are 14,100 and 14,200. One of these is going to be our
answer. Let’s mark the halfway point
again. Halfway between 14,100 and 14,200
is 14,150.
Now, to help us work out whether to
round our number up or down, we need to look at the digit to the right of the
hundreds digit. The tens digit in our number is an
eight. Fourteen thousand one hundred and
eighty something is larger than 14,150. It’s probably about here on our
number line. This time, we’re going to need to
round up.
In this question then, we had a go
at taking the same number but rounding it in different ways. And we thought about how number
lines can help us. If we round 14,189 to the nearest
ten thousand, we get the answer 10,000. If we round the same number to the
nearest thousand, we get 14,000. And if we round it to the nearest
hundred, we get the answer 14,200.
Round 80,531 to the nearest
thousand.
We could use a number line to help
us solve this problem. For us to be able to round 80,531
to the nearest thousand, we need to know what the two multiples of a thousand either
side of this number are. To help us, we can start by looking
at the thousands digit itself. In this number, it’s a zero. This tells us that our number comes
somewhere between 80,000 and 81,000. One of these numbers is going to be
our answer, but which one?
Before we continue, let’s mark the
halfway point on our number line. Halfway is 80,500. Now, to work out where our number
belongs on this number line and whether to round it up or down, we need to look at
the digit to the right of the thousands digit. The hundreds digit is a five. Our number is eighty thousand five
hundred and something. This means we could say it’s about
here on our number line, just past halfway. We can see we’re going to need to
round it up to the nearest thousand. 80,531 rounded to the nearest
thousand is 81,000.
So far, we’ve used number lines to
help us. But do we have to sketch a number
line every single time that we want to round something? Not at all. We can use what we know about place
value instead. Let’s see how.
What is the smallest whole number
that when rounded to the nearest hundred gives a result of 95,200?
Often when we’re asked a question
about rounding numbers, we’re given a number and asked to round it up. But in this question, we need to
think backwards. We’re given the answer, the rounded
number, but we need to find the smallest whole number that will round to this number
when we round it to the nearest hundred.
To begin with then, let’s think
about the rounded number that we have. 95,200 is made up of nine lots of
10,000, five 1,000s, and two 100s. Now, as we’ve said already, this is
the number after another number has been rounded to the nearest hundred. So to begin with, we need to think
about our hundreds digit. It’s been rounded to a two. But what could it have been?
Well, there’s only two possible
answers to that question. It could’ve been a one, and our
starting number could be ninety-five thousand one hundred and something, in which
case our number would’ve been rounded up to 95,200. Or the hundreds digit could be a
two, ninety-five thousand two hundred and something, in which case we’d be rounding
down to 95,200. But let’s not forget we’re looking
for the smallest whole number. The hundreds digit we’re looking
for then is one. But how many tens should our number
have?
Do you remember the rule about
digits for rounding? If a digit is four or less, we
round down. And if a digit is five or more, we
round up. If our tens digit was a nine, for
example, our number would be ninety-five thousand one hundred and ninety
something. This would round to 95,200. But we can go smaller than the nine
in the tens place because an eight would round up too, and a seven, a six, and we
can go one lower because we know if a digit is five or more, we round up. So the lowest possible tens digit
is five. Ninety-five thousand one hundred
fifty something is definitely going to round up to 95,200. It doesn’t matter what the ones
digit is. It’s still going to round to the
number we want.
But wait a moment! It does matter what the ones digit
is because we’re looking for the smallest whole number. There’s no point putting the digit
nine in there. We could go lower than that. We need to put the smallest
possible value digit, which is a zero, 95,150. Now, we know that 95,150 is
actually exactly halfway between 95,100 and 95,200. But with rounding, when we’re
looking at a number exactly at the halfway point, we always round up. We’ve looked at the value of each
digit in a five-digit number and used this to help us think about rounding. The smallest whole number that if
we rounded to the nearest hundred will give us a result of 95,200 is the number
95,150.
So what have we learned in this
video? We’ve learned how to round whole
numbers within one hundred thousand using number lines and thinking about each
digit’s value.
