Video Transcript
Rounding to the Nearest 10
In this video, we’re going to learn
how to round three-digit whole numbers to the nearest 10. Now in maths, if we round a number,
it’s a way of saying about how much it’s worth, not the exact amount, but about that
amount. And if you keep your ears open,
it’s the sort of thing that we hear a lot in everyday life. Someone might say we’ve got roughly
150 kilometers to go, when perhaps the exact distance on the sign you’ve just driven
past says 153 kilometers. Or somebody might say, “It took me
about 40 minutes to get to town,” when it actually took 39 minutes.
We round numbers up all the
time. And if we hear words like “roughly”
or “about,” this sometimes means that our number has been rounded. And there’s something interesting
about the numbers that we usually round to. If we look at the two numbers in
these examples, 150 and 40, they both end in a zero. Numbers that end in a zero are
multiples of 10 and they’re easy to deal with. And in this video, we’re going to
be learning how to do exactly what these two people have done, round numbers to the
nearest 10. And we’re going to be using
three-digit numbers. So let’s start off with an example
that’s all about rounding a three-digit number.
Let’s imagine that someone’s
playing a computer game and they’ve scored 763 points. And then a friend asks us, “About
how many points have you scored?” Now by the way that they’ve asked
this question, we know that they don’t want an exact number, just a rough idea. So we could round 763 to the
nearest 10. One way we can do this is using a
number line. Now eventually, we want to put the
number 763 on this number line. But to begin with, we need to ask
ourselves a question about this number. Which multiples of 10 does this
number belong in between? For a clue, we could look at the
tens digit of this number, which is a six.
This tells us that the nearest
multiple of 10 before we get to this number must be 760 and the nearest multiple of
10 after this number must be when this six turns to a seven, 770. Now to round this number, we need
to think to ourselves, is 763 nearer to 760 or 770? Now it’s always helpful to mark the
halfway point on a number line like this. Halfway between 760 and 770 is
765. Now we’ve got a better idea of
where 763 belongs. We know that 763 is less than 765,
the halfway point. And so we can now see whether we
need to round our number up or down to the nearest 10. 763 is nearest to 760. And so in answer to our friend’s
question, we could just say, “About 760.” 763 rounded to the nearest 10 is
760.
Let’s imagine we carry on playing
the game, and a new score flashes up and our friend asks us the same question. About how many points have you
scored? This time, our score is 825, so we
need to sketch a number line and think about where this number belongs. Remember, first of all, we can ask
ourselves, which two multiples of 10 is this number in between? The tens digit is a two. This gives us a clue as to what the
first multiple of 10 is. The nearest multiple of 10 less
than 825 is 820. And the nearest multiple of 10
larger than 825 will be when those two tens turn into three tens. It’s 830.
And you remember the third thing
that we can do. We can think about the halfway
point in our number line. What number is halfway between 820
and 830? It’s 825. This is interesting. The number that we want to round is
exactly halfway between two multiples of 10. What are we gonna do? We’re going to round it down or
up? Well, there’s a rule here that we
can use to help us. And we need to remember it when it
comes to rounding. If a number is exactly halfway
between two multiples of 10, in other words, if it ends in a five, we always round
it up. 825 rounded to the nearest 10 is
830.
We’re doing a lot of looking at
digits here, aren’t we? Perhaps there’s a way we could
round numbers using place value to help. And being as we’re about to talk
about place value, let’s use place value blocks to make a three-digit number. What’s this number rounded to the
nearest 10? We can see that this number is made
up of two hundreds, four tens, and six ones. This is the number 246. Now without drawing a number line,
which part of this number should we be looking at first? Well, it’s probably a good idea to
start looking at the tens digit. This is going to give us a clue as
to which tens digits we either need to round down or up to. Which multiples of 10 this number
lives in between? Our tens digit here is a four, and
this tells us that we’re either going to have to around our number down to 240 or up
to 250.
Now which part of our number do we
need to look at next? It’s the ones digit. This is going to tell us whether to
round down or to round up. And you remember in our last
example, we had a number that ended in a five. And we said there was a rule for
this, and that number that end in a five in the middle of two multiples of 10 always
round up. And if we know that numbers that
end in a five round upwards, we can include some other digits too, any number that
has a ones digit of five or more — so that’s five, six, seven, eight, or nine — we
round up. And so we know that any number that
has a ones digit of four or less — so that’s four, three, two, or one — we round
down.
Now there’s one digit we haven’t
just mentioned, and that’s a zero. Can you spot why? A number that ends in a zero
already is a multiple of 10. We can’t round it up or down; it
is. So this is a really important rule
to remember: four or less and we round down, five or more and we round up. And we can see in this particular
number, we have six ones. And of course, six is greater than
five. So we know we’re going to have to
round this number up. So we can say 246 rounded to the
nearest 10 is 250. Let’s see what you’re like at
rounding three-digit numbers to the nearest 10. We’re going to try some questions
where you need to practice these skills.
To round three-digit numbers to the
nearest 10, use a number line. Think about the number 437. We can add in the midpoint to help
us. Which two multiples of 10 is 437
between? Hint: We use the digit in the tens
place to guide us. What is 437 rounded to the nearest
10? Hint: Think about which side of the
midpoint 437 will be on.
This question is all about rounding
three-digit numbers. When we round a number, we say
about what it’s worth. And in this question, we’re
rounding numbers to the nearest 10. One way we can do this and the way
that this question gets us to do this is by using a number line. And we’re told to think about the
number 437. Now, if we want to round the number
437 to the nearest 10, we’re going to need to draw a number line where this number
belongs. So our number belongs somewhere on
this line.
Now, the first part of this
question asks us, which two multiples of 10 is 437 between? The number 437 lives or belongs in
between two multiples of 10, numbers that end in a zero. And the first thing we can do on
our number line is to label these two multiples of 10. Now we’re given a hint here. We’re told that we can use the
digit in the tens place to guide us. Now we know the number 437 is made
up of four hundreds, three tens, and seven ones. And so the tens digit that we can
use to guide us is three. This tells us that the number 437
come somewhere between the number 430 and then when these three tens turn to four
tens, 440. So now that we know the number 437
is in between 430 and 440, we need to decide whether to round it up or down.
What is 437 rounded to the nearest
10? Again, we’re given a hint to help
us here. And we’re told to think about which
side of the midpoint 437 will be on. Did you notice the word “midpoint”
as we read the question through? If we look right at the beginning
of the question when we were given that number line to help us, we can see that the
middle of the line has been marked in pink. And it’s also been labeled. We can add in the midpoint to help
us. So let’s do this on our number line
that we’ve sketched. The midpoint is about here. Now what number is in the middle of
430 and 440? It’s 435. And labeling the midpoint like this
can really help us work out whether our number is nearer to 430 or 440.
Where would we put 437 on our
number line? 437 comes after 435. It’s a greater number. And because we can see that it’s on
this side of the midpoint, we can see which multiple of 10 it’s nearest to. We’re going to need to round this
three-digit digit number up. We’ve used a number line to help us
round a three-digit number to the nearest 10. The two multiples of 10 that 437 is
in between are 430 and 440. And we used a midpoint to help us
work out which one of these numbers our number was closest to. 437 rounded to the nearest 10 is
440.
The teacher asked Michael and David
to round the number 572 to the nearest 10. Michael said, “The answer is
570.” David said, “The answer is
580.” Who is correct?
What’s happening in this question
is the sort of thing that might happen in your maths lessons. A teacher has asked a question, but
we’re getting two different answers from two different people. Who is correct? Now the task that both Michael and
David have tried to do in this question is to around the number 572 to the nearest
10. And we’re given two possible
answers. Either Michael’s right when he said
the answer is 570 or David’s right when he said 580. One way we could find the answer is
to look at the place value of the number that we’re rounding. Now we know that the number 572 is
made up of five hundreds, seven tens, and two ones.
Now the first thing we can do with
the digits of this number is look at that tens digit. This gives us an idea of the two
multiples of 10 that this number lives in between. We can take this digit as it is but
change the ones digit for a zero. This gives us the multiple of 10
that is less than our number, 570. And then we can add one to this
digit to make it eight tens. And this would give us the multiple
of 10 that’s larger than our number, 580. Our number is in between 570 and
580. And you can see that this is where
Michael and David have both got their answers from. Michael has thought to himself, I
need to round this number down. And David has rounded the number
up. And to find out who’s correct, we
need to look at another of the digits in our number.
This is the ones digit. Now there’s a rule for ones digits
and rounding to the nearest 10. Do you remember what it is? If the ones digit is four or less —
so that’s four, three, two, or one — we round down. And if the number ends in a five or
more — so that’s five, six, seven, eight, or nine — we round up. Now that we’ve remembered this
rule, we can apply it to this number. The number of ones in 572 is
two. And this is definitely four or
less, isn’t it? So we need to round down. 572 rounded to the nearest 10 must
be 570. We’ve used place value and our
knowledge of rounding to round 572 to the nearest 10. The answer is 570. So the person who is correct is
Michael.
Which of the following numbers can
be 230 when rounded to the nearest 10? 237, 224, 228, or 220.
Each of the possible answers to
this question is a three-digit number. And this question is all about
rounding numbers like these to the nearest 10. Now often, with questions like
these where we have to round numbers, we’re given a number, and then we have to
round that number to the nearest 10. But this question is slightly
different. In this question, we’re given a
multiple of 10. That’s the number 230 in our
question. And we need to find the number that
rounds to this multiple of 10. So in a way, we’re sort of working
backwards here. If we were asked to round each of
these numbers, which one would we round to 230? Well, there are only four answers
to choose from, and one of them we can cross off straightaway. Can you spot which one?
Our last answer is a multiple of 10
already; it’s 220. So we would never need to round
this number to the nearest multiple of 10. It is a multiple of 10. This leaves us with only three
possible answers. Now we know that the number 237 is
in between two multiples of 10, 230 and 240. So do you think we need to round
this number down to 230 or up to 240? Well, if we look at the ones digit
of our number, we can see it’s a seven. And we know that any number that
has a ones digit of five or more, we round up. 237 rounded to the nearest 10 is
240 not 230.
Our next three-digit number is
224. We can draw this on the same number
line, but we are going to have to extend it in one direction here because we know
224 is in between 220 and 230. And the ones digit of this number
is a four. Now, whilst any number that ends in
a five, six, seven, eight, or nine we round up, any number that ends in a four or
less we round down. And so 224 rounded to the nearest
10 is going to be 220 not 230. So this only leaves us with one
possible answer. We know that 228 is in between 220
and 230. But this time, the digit is five or
more, so we can round up. The number that we write as 230
when we round it to the nearest 10 is 228.
What have we learned in this
video? We’ve learned how to round
three-digit whole numbers to the nearest 10. We have used number lines and our
knowledge of place value to help us.
