Lesson Video: Estimating Sums of Three-Digit Numbers: Rounding Mathematics • 3rd Grade

Video Transcript

Estimating Sums of Three-Digit Numbers: Rounding

In this video, we will learn how to round to the nearest ten or hundred to estimate the value of sums up to 1,000.

When we’re adding two three-digit numbers, we can estimate the answer quickly. We can estimate by rounding our three-digit numbers to the nearest hundred. We’ve rounded 142 to 100 and 283 to 300. It’s really easy and quick to add 100 and 300, so our estimate is 400. We’re also going to learn how to round to the nearest ten to help us estimate the sums of two three-digit numbers. We would round 142 to 140, because that’s the nearest ten. And if we round 283 to the nearest ten, we would get 280. Then we can add 140 and 280 to give us an estimate of 420.

Before we start to practice estimating sums, in this video we’re going to be estimating by rounding to the nearest ten or hundred. Before we start answering questions, we need to practice the skill of rounding.

We need to round the number 726 to the nearest ten. We need to use our knowledge of place value to help round to the nearest ten. We can see that the number 726 has two 10s, worth 20. And we know that 726 comes after 720 and before 730. The two 10s that 726 is between are 720 and 730. Let’s mark our number on the number line. 725 is the midway point between our two multiples of 10. It’s halfway between 720 and 730. And we know that 726 is one more than 725, so we can mark it here on the number line.

To help us decide which ten we need to round our number to, we need to look to the digit to the right of the tens digit. In other words, to round to the nearest ten, we need to look at the ones digit. The ones digit in 726 is a six. If the ones digit is five or more, we have to round up. We know that six is more than five, so we have to round our number up. The nearest ten to 726 is 730.

Let’s try rounding 723 to the nearest ten. Again, our number comes between 720 and 730, and the ones digit is a three. 723 would go here on the number line. When we’re rounding to the nearest ten, if the ones digit is less than five, we have to round down. The nearest ten to 723 is 720.

Now let’s practice rounding 387 to the nearest hundred. The first thing we need to decide is which two hundreds numbers 387 lies between. 387 has three 100s, so we know our number lies between 300 and 400. When we’re rounding to the nearest hundred, we need to look at the tens digit. We’ve placed number 387 on the number line, and we can see that it has eight 10s. If the tens digit is worth five or more, we round up. So the nearest hundred to 387 is 400.

Now that we’ve practiced rounding three-digit numbers to the nearest ten or hundred, let’s try some questions where we need to add two three-digit numbers by rounding to the nearest ten or hundred to estimate the answer.

Choose the number that is closest to 110 plus 368. Is it 600, 500, or 400?

In this question, we’re being asked to estimate the sum of 110 and 368. And each of the estimates is a multiple of 100: 600, 500, and 400. So we need to round 110 and 368 to the nearest hundred. Let’s start by rounding 110 to the nearest hundred. The hundreds digit in the number 110 is a one. So we know 110 comes after 100. And the next hundred after 100 is 200. And 110 would come here on our number line. When we’re rounding to the nearest hundred, we have to look at the tens digit. If the tens digit is less than five, we have to round down. So the nearest hundred to 110 is 100.

Next, we need to round the number 368 to the nearest hundred. 368 has three 100s, so we know 368 comes after 300, and the next hundred is 400. We can mark 368 here on our number line. When we’re rounding a three-digit number to the nearest hundred, we have to look at the tens digit. If the tens digit is five or more, we have to round up. And we know that six is greater than five, so we need to round up to 400. The nearest hundred to 368 is 400.

Now we’ve rounded both of our three-digit numbers to the nearest hundred. We can go ahead and add them together. 100 plus 400 is 500. The number that is closest to 110 and 368 is 500. We estimated the sum of 110 and 368 by rounding both numbers to the nearest hundred. 110 and 368 is about 500.

Look at this calculation: 572 plus 241. Estimate the answer by rounding both numbers to the nearest hundred. Estimate the answer by rounding both numbers to the nearest ten. Find the exact answer. Tip: Use the estimates to see if your answer is sensible.

This is a three-part question. First, we have to estimate the answer to 572 plus 241 by rounding both numbers to the nearest hundred. Then we need to estimate the answer by rounding both numbers to the nearest ten. And then we have to find the exact answer. Let’s start by rounding both numbers to the nearest hundred.

The number 572 has five 100s. So we know our number is worth more than 500. And the next hundred after 500 is 600. So we know that 572 comes somewhere between 500 and 600. But which is the nearest hundred? When we’re rounding a three-digit number to the nearest hundred, we have to look at the tens digit. If the tens digit is worth five or more, we have to round up. The tens digit in 572 is a seven, and we know that seven is worth more than five. So we need to round up to 600. 572 rounded to the nearest hundred is 600.

Now let’s round 241 to the nearest hundred. 241 has two 100s, so our number lies between 200 and 300. But which is the nearest hundred? Again, we need to look to the tens digit. And we know if the tens digit is less than five, we need to round down. 241 to the nearest hundred is 200.

Now all we need to do is add 600 and 200. Our estimated answer is 800.

Now we need to estimate the answer by rounding both numbers to the nearest ten. 572 has seven 10s, worth 70. So we know that 572 comes between 570 and the next ten, which is 580. But which is the nearest ten, 570 or 580? When we’re rounding to the nearest ten, we need to look to the ones digit. If the ones digit is less than five, we have to round down. So the nearest ten to 572 is 570.

Now we need to round 241 to the nearest ten. 241 has four 10s, worth 40. So we know 241 comes between 240 and 250. And again, we need to look to the ones digit. One is less than five, so we need to round down. The nearest ten to 241 is 240.

Now we just need to add 570 and 240 to give us our estimated answer. Zero plus zero is zero. Seven 10s and four 10s are 11 10s. Five 100s plus two 100s is 700, plus the one we exchanged gives us a total of eight 100s. We’ve rounded both of our numbers to the nearest ten, and our estimated answer is 810.

Now all we need to do is find the exact answer. We need to add 572 and 241. Let’s start by adding the ones. Two plus one is three. Seven 10s plus four 10s gives us 11 10s. We’ve got a total of seven 100s plus the one we exchanged, which gives us eight 100s. The exact answer is 813, which is very close to our estimate of 800 and 810.

We rounded both numbers to the nearest hundred, which gave us an estimated answer of 800. Then we rounded both numbers to the nearest ten, which gave us an estimate of 810. Then we found the exact answer of 813.

Amelia won 586 tickets at the fair. Her sister won 379. Pick the best estimate for the total number of tickets that they won. 800, 1,000, 200, 900, or 600.

In this question, we have to estimate the total number of tickets that Amelia and her sister won at the fair. We know Amelia won 586 tickets and her sister won 379 tickets. To estimate the total number of tickets they won, we need to round both of our numbers to the nearest hundred. This is because each of our possible estimates is a multiple of 100: 800, 1,000, 200, 900, and 600.

Let’s start by rounding 586 to the nearest hundred. 586 has five 100s, so we know this number comes between 500 and 600. We could place number 586 roughly here on our number line. Which is the nearest hundred, 500 or 600? To help us round to the nearest hundred, we need to look at the tens digit. 586 has eight 10s. And we know if the tens digit is five or more, we have to round up. Since eight is greater than five, we need to round up to 600. 586 rounded to the nearest hundred is 600.

Now we need to round 379 to the nearest hundred. 379 is between 300 and 400. We would place the number 379 here on the number line. When we’re rounding to the nearest hundred, we need to look at the tens digit of our number. It’s a seven. And we know if the tens digit is worth five or more, we have to round up. So the nearest hundred to 379 is 400.

Now all we need to do is find the sum of our two numbers, 600 plus 400. 600 plus 400 is 1,000. The best estimate for the total number of tickets that Amelia and her sister won at the fair is 1,000. We rounded 586 to 600. We rounded 379 to 400. And 400 plus 600 is 1,000.

What have we learned in this video? We’ve learned how to estimate the sum of two three-digit numbers by rounding to the nearest ten or one hundred.