Video Transcript
Estimating Sums and Differences:
Four-Digit Numbers
In this video, we’re going to learn
how to estimate sums and differences between numbers with up to four digits by
rounding to the nearest ten, hundred, and thousand.
Ben and Mia are playing a computer
game together. Ben’s highest score is 1,873, and
Mia’s highest score is 3,025. The children want to know roughly
how many points they have scored altogether. When we hear the words roughly or
approximately or about, we know we don’t need to find the exact answer; we need to
find the estimated answer. To help us estimate 1,873 plus
3,025, let’s round both of our four-digit numbers to the nearest thousand. In this video, we’re going to learn
two different ways to round numbers, either to the nearest thousand, hundred, or
ten. We’re going to use our knowledge of
place value and number lines to help us round.
Let’s start with the number
1,873. We know it has one in the thousands
place, worth 1,000. So this number comes between 1,000
and 2,000. Each of our divisions is worth
100. The hundreds digit in 1,873 is an
eight, worth 800. So let’s start at 1,000 on our
number line and count forward until we reach 1,800. 1,100, 1,200, 1,300, 1,400, 1,500,
1,600, 1,700, 1,800, and here’s 1,900. Where would we place 1,873 on the
number line? Here we go, about here. The nearest thousand to 1,873 is
2,000.
Let’s round 3,025 to the nearest
thousand now. The thousands digit is a three, so
we know this number is between 3,000 and 4,000. And the number which is halfway
between these two numbers is 3,500. The hundreds digit in this number
is a zero. It has no hundreds. 3,025 would go roughly here on the
number line, between 3,000 and 3,100. It’s really easy to see that 3,025
is nearest to 3,000. Ben and Mia scored roughly 5,000
points altogether.
When we’re rounding to the nearest
thousand, we have to use the hundreds digit to help us. If the hundreds digit is worth a
five or more, we have to round up. And if the hundreds digit is worth
less than five, we have to round down. If we wanted to estimate the
difference between Ben and Mia’s scores, we would round both numbers to the nearest
thousand and subtract 2,000 from 3,000. The difference is 1,000.
The actual sum of Ben and Mia’s
score is 4,898, and the estimated sum is 5,000, which is pretty close to 4,898. It’s a good estimate. So far in this video, we’ve learned
how to round two four-digit numbers to the nearest thousand to help us estimate the
sum or the difference. Let’s put into practice what we’ve
learned now and have a go and answering a question where we need to round our
numbers to the nearest thousand.
Which number is nearest to 4,877
plus 3,103. Is it 10,000, 7,000, 9,000, 6,000,
or 8,000?
In this question, we have to say
which multiple of 1,000 is nearest to the sum of our two four-digit numbers. Let’s round both of these
four-digit numbers to the nearest thousand to estimate the sum. We can use a place value table to
help us round. We’re rounding to the thousands
place. The thousands digit in 4,877 is a
four. So we know our number comes between
4,000 and 5,000. We need to look at the hundreds
digit to help us decide whether to round up or down. The hundreds digit is an eight. If this digit is worth five or
more, we have to round up. Eight is greater than five. So we need to round 4,877 up to
5,000.
Now we need to around 3,103 to the
nearest thousand. The thousands digit is a three. So our number comes between 3,000
and 4,000. The hundreds digit is a one. And we know if this digit is less
than five, we have to round down. 3,103 rounded to the nearest
thousand is 3,000. Now we can estimate this sum. What is 5,000 plus 3,000? It’s 8,000.
Let’s quickly check this is a good
estimate by finding the actual answer. 4,877 plus 3,103 is 7,980. Let’s round this number to its
nearest thousand. The thousands digit is a seven, so
we know our number is between 7- and 8,000. The hundreds digit is a nine, which
is greater than five, so we have to round up. The number which is nearest to
4,877 plus 3,103 is 8,000. We rounded both of our four-digit
numbers to the nearest thousand and then estimated the sum.
Earlier in this video, we learned
how to round numbers to the nearest thousand to help us estimate sums and
differences. And we estimated Ben and Mia’s
total score to be around 5,000. What if we were to round 1,873 and
3,025 to the nearest hundred? How would that affect our
estimate?
When we’re rounding to the hundreds
place, we use the tens digit to help us decide whether to round up or down. And we know that if the tens digit
is less than five, we have to round down. And if the tens digit is equal to
or greater than five, we have to round up. The tens digit in the number 1,873
is a seven. Seven is greater than five, so we
round 1,873 up to 1,900. And the tens digit in the number
3,025 is a two. Two is less than five, so we round
down to 3,000. 3,000 is a multiple of 100. And our number 3,025 comes between
3,000 and 3,100. So the nearest hundred to 3,025 is
also the nearest thousand.
So the actual sum of Ben and Mia’s
score is 4,898. By rounding to the nearest
thousand, we estimated the sum to be 5,000. And by rounding to the nearest
hundred, we estimated the sum to be 4,900. Which is the closest estimate? It’s 4,900. Let’s round both of our four-digit
numbers to the nearest ten.
When we round to the tens place, we
have to look to the digit to the right, which is the ones digit, to help us decide
whether to round up or down. 1,873 has seven 10s, so we know
this number comes between 1,870 and 1,880. The ones digit is a three. Three is less than five, so we
round down to 1,870. Let’s round 3,025 to the nearest
ten. The tens digit is a two or 20, so
we know that 3,025 is between 3,020 and 3,030. The ones digit is five, so we have
to round up to 3,030. If we round both our numbers to the
nearest ten and find the sum, it’s 4,900.
So we’ve learned how to round to
the nearest thousand, hundred, and ten to help us estimate sums or differences. And we found the most accurate
estimates by rounding to the nearest hundred or ten. Let’s practice a couple more
questions now where we need to round to the nearest hundred or the nearest ten.
Estimate 3,638 take away 361,
rounding each number to the hundreds place.
In this question, we have to
estimate the difference by rounding each of our numbers to the hundreds place. In other words, we have to round
both numbers to the nearest hundred. Let’s start by rounding 3,638. We have to round to the hundreds
place. The hundreds digit in our number is
a six, worth 600. So we know 3,638 is between 3,600
and 3,700. To help us decide whether to round
our number down to 3,600 or up to 3,700, we have to look at the tens digit. It’s a three. We know that three is worth less
than five, so we have to round down to 3,600.
Now we have to round 361 to its
nearest hundred. The hundreds digit is a three. And that’s worth 300. So we know 361 is between 300 and
the next hundred, which is 400. And again, we need to look at the
tens digit to help us decide whether to round down to 300 or up to 400. The tens digit is a six. Six is greater than five, so we
have to round up to the next hundred, which is 400. Now all we need to do is find the
difference between 3,600 and 400. 3,600 subtract 400 is 3,200.
We estimated 3,638 take away 361 by
rounding each number to the hundreds place. Then we calculated 3,600 take away
400 to give us our estimate of 3,200.
Estimate 2,145 plus 123 by rounding
each number to the tens place.
In this question, we have to
estimate the sum of our two numbers by rounding each number to the nearest ten. Let’s start by rounding 2,145 to
the nearest ten. The tens digit in 2,145 is a four,
worth 40. So we know 2,145 comes between
2,140 and 2,150. So to help us decide whether to
round our number down to 2,140 or up to 2,150, we need to look to the ones
digit. The ones digit is a five. If the ones digit is worth five or
more, we have to round up to 2,150. So the nearest 10 to 2,145 is
2,150. We had to round up.
Let’s round our next number to the
nearest ten. The tens digit in 123 is a two,
worth two 10s. So we know the two 10s our number
is between are 120 and 130. To help us decide whether to round
down to 120 or up to 130, we need to look at the ones digit. We know that three is less than
five, so we have to round down to 120. Now all we need to do is add
together 2,150 and 120, which is 2,270. We estimated 2,145 plus 123 by
rounding each number to the tens place. Our estimate is 2,270.
What have we learned in this
video? We’ve learned how to estimate sums
and differences between numbers with up to four digits by rounding to the nearest
ten, hundred, and thousand.
